**Journal Articles**

Qingxia Liu, Pinghui Zhuang, Fawang Liu*, Minling Zheng and Shanzhen Chen (2021) Radial point interpolation collocation method based approximation for 2D fractional equation models.

*Computers and Mathematics with Applications*. (https:// doi.org/10.1016/j.camwa.2021.05.007)Xingyu An, Fawang Liu*, Minling Zheng, Vo V. Anh, Ian W. Turner, (2021) A space-time spectral method for time fractional Black-Scholes equation.

*Applied Numerical Mathematics*.Hui Zhang, Xiaoyun Jiang*, Fawang Liu, (2021) Error analysis of nonlinear time fractional mobile/ immobile advection-diffusion equation with weakly singular solutions.

*Fractional Calculus and Applied Analysis*. (DOI: 10.1515/fca- 2021-0009.)Tao Xu, Fawang Liu*, Shujuan Lv, Vo V. Anh, (2021) Numerical approximation of a 2D multi-term time and space fractional Bloch-Torrey. equations involving the fractional Laplacian.

*Journal of Computational and Applied Mathematics*.Yuli Chen , Fawang Liu*, Qiang Yu , Tianzeng Li (2021) Review of fractional epidemic models.

*Applied Mathematical Modelling*. (https://doi.org/10.1016/j.apm.2021.03.044)Weidong Yang, Xuehui Chen*, Xinru Zhang, Liancun Zheng, (2021) Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship,.

*Computers and Mathematics with Applications*. (https://doi.org/10.1016/j.camwa.2021.04.023)Tao Xu, Fawang Liu*, Shujuan Lu, Vo Anh, (2020) Finite difference/finite element method for twodimensional time-space fractional Bloch-Torrey equations with variable coefficients on irregular convex domains.

*Computers and Mathematics with Applications*. (https:// doi.org/10.1016/j.camwa.2020.11.007.)Z. Yang, F. Liu*, Y. Nie, I. Turner, (2020) An Unstructured mesh finite difference/finite element method for the three-dimensional time-space fractional Bloch-Torrey equations on irregular domains.

*Journal of Computational Physics*. (https:// doi.org/10.1016/j.jcp.2020.109284.)R. Zheng, F. Liu*, X. Jiang, (2020) A Legendre spectral method on graded meshes for the twodimensional multi-term time-fractional diffusion equation with non-smooth solutions.

*Applied Mathematics Letters*. (https://doi.org/10.1016/j.aml.2020.106247)R. Zheng, F. Liu*, X. Jiang, I. Turner, (2020) Finite difference/spectral methods for the twodimensional distributed-order time-fractional cable equation.

*Computers and Mathematics with Applications*. (https://doi.org/10.1016/j.camwa.2020.06.017)L. Feng, F. Liu*, I. Turner, (2020) An unstructured mesh control volume method for twodimensional space fractional diffusion equations with variable coefficients on convex domains.

*Journal of Computational and Applied Mathematics*. (https:// doi.org/10.1016/j.cam.2019.06.035.)Q. Liu, P. Zhuang, F. Liu*, J. Lai, V. Anh and S. Chen, (2020) An investigation of radial basis functions for fractional derivatives and their applications.

*Computational Mechanics*. (https://doi.org/10.1007/s00466-019-01779-z.)W. Yang, X. Chen, X. Zhang, L. Zheng and F. Liu*, (2020) Flow and heat transfer of double fractional Maxwell fluids over a stretching sheet with variable thickness.

*Applied Mathematical Modelling*. (https://doi.org/10.1016/j.apm.2019.11.017.)B. Li and F. Liu*, (2020) Boundary Layer Flows of Viscoelastic Fluids over a non-uniform Permeable Surface.

*Computers and Mathematics with Applications*. (https:// doi.org/10.1016/j.camwa.2019.11.003.)S. Yang, F. Liu*, L. Feng, I. Turner, (2020) Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients.

*Applied Numerical Mathematics,*. (https://doi.org/10.1016/j.apnum.2020.05.016)S. Yang, F. Liu*, L. Feng, I. Turner, (2020) A novel finite volume method for the nonlinear two-sided space distributed-order diffusion equation with variable coefficients.

*Journal of Computational and Applied Mathematics*.M. Mahiuddin, D. Godhani, L. Feng, F. Liu, T. Langrish, M. Karim, (2020) Application of Caputo fractional rheological model to determine the viscoelastic and mechanical properties of fruit and vegetables.

*Postharvest Biology and Technology*.R. Chen, X. Wei, F. Liu*, Vo Anh, (2020) Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete.

*Philosophical Transactions A*. (https://doi.org/10.1098/rsta.2019.0538.)Y. Wang, F. Liu*, L. Mei, V. Anh, (2020) A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions.

*Numerical Algorithms*. (DOI: 10.1007/s11075-020-00940-7)X. Gao, F. Liu*, H. Li, Y. Liu, I. Turner, B. Yin, (2020) A novel finite element method for the distributed-order time fractional Cable equation in two dimensions,.

*Computers and Mathematics with Applications*. (doi.org/10.1016/j.camwa.2020.04.019.)Xingyu An, F. Liu*, Shanzhen Chen, Vo V. Anh, (2020) Novel Numerical Techniques for the Finite Moment Log Stable Computational Model for European Call Option.

*Numerical Methods for Partial Differential Equations*.Junjiang Lai, Fawang Liu, V. Anh, Qingxia Liu, (2020) A space-time finite element method for solving linear Riesz space fractional partial differential equations.

*Numerical Algorithms*.Y. Liu, Y. Du, H. Li, F. Liu*, Y. Wang (2019) Some second-order $\theta$ schemes combined with finite element method for nonlinear fractional Cable equation.

*Numerical Algorithms*. (https://link.springer.com/article/10.1007/s11075-018-0496-0)Ruige Chen, Fawang Liu, Vo Anh (2019) Numerical methods and analysis for a multi-term time–space variable-order fractional advection–diffusion equations and applications.

*Journal of Computational and Applied Mathematics*. (https://eprints.qut.edu.au/124205/)Libo Feng, Fawang Liu, IanTurner (2019) Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains.

*Communications in Nonlinear Science and Numerical Simulation*. (https://www.sciencedirect.com/science/article/pii/S1007570418303307)Zeting Liu, Fawang Liu, Fanhai Zeng (2019) An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations.

*Applied Numerical Mathematics*. (https://www.sciencedirect.com/science/article/pii/S0168927418302307)Shujun Shen, Fawang Liu, Vo V. Anh (2019) The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation.

*Journal of Computational and Applied Mathematics*. (https://www.sciencedirect.com/science/article/pii/S0377042718302917)X Chen, W Yang, X Zhang, F Liu (2019) Unsteady boundary layer flow of viscoelastic MHD fluid with a double fractional Maxwell model.

*Applied Mathematics Letters*. (https://www.sciencedirect.com/science/article/pii/S0893965919301454)R Chen, F Liu, V Anh (2019) A fractional alternating-direction implicit method for a multi-term time-space fractional Bloch-Torrey equations in three dimensions.

*Computers & Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122118306886)T Li, Y Wang, F Liu, I Turner (2019) Novel parameter estimation techniques for a multi-term fractional dynamical epidemic model of dengue fever.

*Numerical Algorithms*. (https://link.springer.com/article/10.1007/s11075-019-00665-2)F Liu, L Feng, V Anh, J Li (2019) Unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains.

*Computers & Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122119300124)M. Zhang, M. Shen, F. Liu, H. Zhang (2019) A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium.

*Computers & Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122119300112)Y. Shi, F. Liu*, Y. Zhao, F. Wang, I. Turner (2019) An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain.

*Applied Mathematical Modelling*. (https://www.sciencedirect.com/science/article/pii/S0307904X19302136)J. Zhang, F. Liu*, V. Anh (2019) Analytical and numerical solutions of a two-dimensional multi-term time-fractional Oldroyd-B model.

*Numerical Methods for Partial Differential Equations*. (https://onlinelibrary.wiley.com/doi/full/10.1002/num.22327)J. Zhang, F. Liu*, Z. Lin, V. Anh (2019) Analytical and numerical solutions of a multi-term time-fractional Burgers' fluid model.

*Applied Mathematics and Computation*. (https://www.sciencedirect.com/science/article/pii/S0096300319301894)R. Chen, F. Liu, V. Anh (2019) Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications. .

R. Chen, F. Liu*, V. Anh, (2019) A fractional alternating-direction implicit method for a multi-term time-space fractional Bloch-Torrey equations in three dimensions. .

Xuehui Chen, Weidong Yang, Xinru Zhang, Fawang Liu, (2019) Unsteady boundary layer flow of viscoelastic MHD fluid with a double fractional Maxwell model.

*Applied Mathematics Letters*.Lang Li, Fawang Liu, Libo Feng, Ian Turner, (2019) A Galerkin finite element method for the modified distributed-order.

*Journal of Computational and Applied Mathematics*.Chunyan Liu, LiancunZ heng, Ping Lin, Mingyang Pan, and Fawang Liu, (2019) Anomalous diffusion in rotating Casson fluid through a porous medium.

*Physica A: Statistical Mechanics and its Applications*.M. Zhang, M. Shen, F. Liu, H. Zhang, (2019) A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium.

*Computers and Mathematics with Applications*.M. Zheng, F. Liu and V. Anh, (2019) An Effective Algorithm for Computing Fractional Derivatives and Applications to Fractional Differential Equations.

*International Journal of Numerical Analysis and Modeling*.S. Qin, F. Liu* and Ian Turner (2018) A two-dimensional multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements.

*Communications in Nonlinear Science and Numerical Simulation*. (https://www.sciencedirect.com/science/article/pii/S1007570417302952)Yang Liu, Zudeng Yu, Hong Li, Fawang Liu*, Jinfeng Wang (2018) Time two-mesh algorithm combined with finite element method for time fractional water wave model.

*International Journal of Heat and Mass Transfer*. (https://www.sciencedirect.com/science/article/pii/S0017931017346847)Yan Zhang, Haojie Zhao, Fawang Liu, Yu Bai (2018) Analytical and numerical solutions of the unsteady 2D flow of MHD fractional Maxwell fluid induced by variable pressure gradient.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122117306934)W. Fan, F. Liu*, X. Jiang, I. Turner (2018) Some novel numerical techniques for an inverse problem of the multi-term time fractional partial differential equation.

*Journal of Computational and Applied Mathematics*. (https://doi.org/10.1016/j.cam.2017.12.034)Lin Liu and F. Liu (2018) Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness.

*Applied Mathematics Letter*. (https://www.sciencedirect.com/science/article/pii/S0893965917303178)Wenping Fan, Fawang Liu* (2018) A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain.

*Applied Mathematics Letter*. (https://www.sciencedirect.com/science/article/pii/S0893965917303142)X. Zhu, Z. Yuan, F. Liu, Y. Nie (2018) Differential quadrature method for space-fractional diffusion equations on 2D irregular domains.

*Numerical Algorithms*. (https://link.springer.com/article/10.1007/s11075-017-0464-0)Y. Li, F. Liu, I. Turner, Tao Li (2018) Time-fractional diffusion equation for signal smoothing.

*Applied Mathematics and Computation*. (https://www.sciencedirect.com/science/article/pii/S0096300318300201)Libo Feng, Fawang Liu*, Ian Turner, Qianqian Yang and Pinghui Zhuang (2018) Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/116276/)S. Chen, F. Liu*, I. Turner and Xiuling Hu (2018) Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium.

*Applied Mathematical Modelling*. (https://www.sciencedirect.com/science/article/pii/S0307904X1830057X)F. Wang, F. Liu*, Y. Zhao, Y. Shi, Z. Shi (2018) A novel approach of high accuracy analysis of anisotropic bilinear finite element for time-fractional diffusion equations with variable coefficient.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122118301111)W. Fan, X. Jiang, F. Liu*, V. Anh (2018) The unstructured mesh finite element method for the two-dimensional multi-term time-space fractional diffusion-wave equation on an irregular convex domain.

*Journal of Scientific Computing*. (https://link.springer.com/article/10.1007/s10915-018-0694-x)Zeting Liu, Shujuan Lv, Fawang Liu (2018) Fully discrete spectral methods for solving time fractional nonlinear Sine-Gordon equation with smooth and non-smooth solutions.

*Applied Mathematics and Computation*. (https://www.sciencedirect.com/science/article/pii/S009630031830242X)Lin Liu, Liancun Zheng, Yu Fan, Yanping Chen and Fawang Liu (2018) Comb model for the anomalous diffusion with dual-phase-lag constitutive relation.

*Communications in Nonlinear Science and Numerical Simulation*. (https://www.sciencedirect.com/science/article/pii/S1007570418300972)Ming Shen, Shurui Chen, Fawang Liu (2018) Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes.

*Chinese Journal of Physics*. (https://www.sciencedirect.com/science/article/pii/S0577907317307992)S. Shen, F. Liu*, V. Anh (2018) The analytical solution and numerical solutions for a two dimensional multi-term time fractional diffusion and diffusion-wave equation.

*Journal of Computational and Applied Mathematics*. (https://www.sciencedirect.com/science/article/pii/S0377042718302917)M Shen, L Chen, M Zhang, F Liu (2018) A renovated Buongiorno’s model for unsteady Sisko nanofluid with fractional Cattaneo heat flux.

*International Journal of Heat and Mass Transfer*. (https://www.sciencedirect.com/science/article/pii/S001793101831161X)L Liu, L Zheng, Y Chen, F Liu (2018) Fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness.

*Journal of Heat Transfer*. (https://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleID=2677512)L Liu, L Zheng, Y Chen, F Liu (2018) Anomalous diffusion in comb model with fractional dual-phase-lag constitutive relation.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122118302141)Y Li, M Jiang, F Liu (2018) Time fractional super-diffusion model and its application in peak-preserving smoothing.

*Chemometrics and Intelligent Laboratory Systems*. (https://www.sciencedirect.com/science/article/pii/S0169743917304513)Z. Shi, Y. Zhao, F. Liu*, F.L. Wang, Y.F. Tang (2018) Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes.

*Applied Mathematics and Computation*. (https://www.sciencedirect.com/science/article/pii/S0096300318305149)L. Liu, L. Zheng, F. Liu, L. Ma (2018) Anomalous diffusion in finite length fingers comb frame subjected with the time and space Riesz fractional Cattaneo-Christov flux and Poiseuille flow.

*Journal of Computational Mathematics*. (https://web.b.ebscohost.com/ehost/detail/detail?vid=0&sid=5fdc6019-3bd4-4fb8-9a25-95aa5eaf75c9%40sessionmgr120&bdata=JkF1dGhUeXBlPWlwLHNzbyZzaXRlPWVob3N0LWxpdmUmc2NvcGU9c2l0ZQ%3d%3d#AN=129988281&db=afh)Shi, Z., Zhao, Y., Liu, Fawang, Wang, F., Tang, Yifa (2018) Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes

*Applied Mathematics and Computation*, 338, pp.290-304. [eprints.qut.edu.au/121061/]Chen, S., Liu, Fawang, Turner, Ian, Anh, Vo (2018) A fast numerical method for two-dimensional Riesz space fractional diffusion equations on a convex bounded region

*Applied Numerical Mathematics*, 134, pp.66-80. [eprints.qut.edu.au/120143/]Zhang, H., Liu, Fawang, Chen, S., Anh, Vo, Chen, J. (2018) Fast numerical simulation of a new time-space fractional option pricing model governing European call option

*Applied Mathematics and Computation*, 339, pp.186-198. [eprints.qut.edu.au/121063/]Zhang, Hui, Liu, Fawang, Jiang, Xiaoyun, Zeng, Fanhai, Turner, Ian (2018) A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space distributed-order advection-diffusion equation

*Computers and Mathematics with Applications*, 76 (10), pp.2460-2476. [eprints.qut.edu.au/121065/]F.A. Abdullah, F. Liu, P. Burrage, K. Burrage, T. Li (2018) Analytical and Numerical Solutions for Fractional Temporal SEIR Measles Model.

*Numerical Algorithms*. (https://link.springer.com/article/10.1007/s11075-017-0426-6)L. Liu, L. Zheng, F. Liu, X. Zhang (2018) Anomalous diffusion in finite length fingers comb frame subjected with the time and space Riesz fractional Cattaneo-Christov flux and Poiseuille flow.

*Journal of Computational Mathematics*.Lin Liu, Liancun Zheng, Yanping Chen, Fawang Liu (2018) Fractional anomalous convection diffusion in comb structure with Non-Fick constitutive model.

*Journal of Statistical Mechanics: Theory and Experiment*. (http://iopscience.iop.org/article/10.1088/1742-5468/aa9dd4/meta)Lin Liu, Liancun Zheng, Yanping Chen, Fawang Liu (2018) Fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness.

*Journal of Heat Transfer*.Lin Liu, Liancun Zheng, Yanping Chen, Fawang Liu (2018) Anomalous diffusion in comb model with fractional dual-phase-lag constitutive relation.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122118302141)Liu, Lin, Zheng, Liancun, Liu, Fawang (2018) Research on macroscopic and microscopic heat transfer mechanisms based on non-Fourier constitutive model

*International Journal of Heat and Mass Transfer*, 127 (Part B), pp.165-172. [eprints.qut.edu.au/121072/]L. Feng, F. Liu, I. Turner, L. Zheng (2018) Novel numerical analysis of multi-term time fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid.

*Fractional Calculus and Applied Analysis*. (https://www.degruyter.com/view/j/fca.2018.21.issue-4/fca-2018-0058/fca-2018-0058.xml)Zheng, Minling, Liu, Fawang, Liu, Qingxia, Burrage, Kevin, Simpson, Matthew (2017) Numerical solution of the time fractional reaction–diffusion equation with a moving boundary

*Journal of Computational Physics*, 338, pp.493-510. [eprints.qut.edu.au/104419/]L Feng, F Liu, I Turner, P Zhuang (2017) Numerical methods and analysis for simulating the flow of a generalized Oldroyd-B fluid between two infinite parallel rigid plates.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/114657/)W. Fan, F. Liu*, X. Jiang and I. Turner (2017) A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain.

*Fractional Calculus & Applied Analysis*. (https://eprints.qut.edu.au/104241/)J. Li, F. Liu*, L. Feng and I. Turner (2017) A novel finite volume method for the Riesz space distributed-order advection-diffusion equation.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/104459/)J. Li, F. Liu*, L. Feng and I. Turner (2017) A novel finite volume method for the Riesz space distributed-order diffusion equation.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/114560/)S. Qin, F. Liu*, I. Turner, V. Vegh, Q. Yu and Q. Yang (2017) Multi-term time-fractional Bloch equations and application in magnetic resonance imaging.

*Journal of Computational and Applied Mathematics*. (https://eprints.qut.edu.au/104460/)L. Liu, L. Zheng, F. Liu, X. Zhang (2017) Heat conduction with fractional Cattaneo–Christov upper-convective derivative flux model.

*International Journal of Thermal Sciences*. (https://eprints.qut.edu.au/101766/)L. Liu, L. Zheng, F. Liu, X. Zhang (2017) Exact solution and invariant for fractional Cattaneo anomalous diffusion of cells in two dimensional comb framework.

*Nonlinear Dynamics*. (https://eprints.qut.edu.au/114624/)L. Liu, L. Zheng, F. Liu (2017) Time fractional Cattaneo-Christov anomalous diffusion in comb frame with finite length of fingers.

*Journal of Molecular Liquids*. (https://eprints.qut.edu.au/104414/)L. Liu, L. Zheng, F. Liu (2017) Temporal evolution characteristics of particles distribution and fractional order moment on backbone of comb model with Cattaneo-Christov flux.

*Journal of Statistical Mechanics: Theory and Experiment*. (http://iopscience.iop.org/article/10.1088/1742-5468/aa64fa/meta)C. Sin, L. Zheng, J. Sin, F. Liu, L. Liu (2017) Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/114628/)J. Zhao, L. Zheng, X. Zhang, F. Liu (2017) Unsteady natural convection heat transfer past a vertical flat plate embedded in a porous medium saturated with fractional Oldroyd-B fluid.

*Journal of Heat Transfer*. (https://eprints.qut.edu.au/104461/)J. Zhao，L. Zheng，X. Chen，X. Zhang，F. Liu (2017) Unsteady Marangoni convection heat transfer of fractional Maxwell fluid with Cattaneo heat flux.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/104277/)Y. Zhao, Y. Zhang, F. Liu*, I. Turner, Y. Tang and V. Anh (2017) Convergence and Superconvergence of A Fully-discrete Scheme for Multi-Term Time Fractional Diffusion Equations.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/101406/)L. Zhao, F. Liu, V. Anh (2017) Numerical methods for the two-dimensional multi-term time-fractional diffusion equations.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S089812211730425X)S. Qin, F. Liu*, I. Turner, Q. Yang and Q. Yu (2017) Modelling anomalous diffusion using fractional Bloch-Torrey equations on two-dimensional approximate irregular domains.

*Computers and Mathematics with Applications*. (https://www.sciencedirect.com/science/article/pii/S0898122117305242)L. Feng, F. Liu*, I. Turner and P. Zhuang (2017) Numerical methods and analysis for simulating the flow of a generalized Oldroyd-B fluid between two infinite parallel rigid plates.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/114657/)M. Pan, L. Zheng, F. Liu, C. Liu, Xuehui Chen (2017) A spatial-fractional thermal transport model for nanofluid in porous media.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/111093/)Y. Bai, Y. Jiang, F. Liu and Y. Zhang (2017) Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation.

*AIP Advences*. (https://aip.scitation.org/doi/abs/10.1063/1.5011789)Z. Yang, Z. Yuan, Y. Nie, J. Wang, X. Zhu, F. Liu (2017) Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains.

*J. Comp Physics*. (https://eprints.qut.edu.au/101610/)S. Chen, F. Liu*, X. Jiang, I. Turner and K. Burrage (2016) Fast finite difference approximation for identifying parameters in a two-dimensional space-fractional nonlocal model with variable diffusivity coefficients.

*SIAM Journal on Numerical Analysis*. (https://eprints.qut.edu.au/101392/)M. Zheng, F. Liu*, V. Anh and I. Turner (2016) A High Order Spectral Method for the Multi-Term Time-Fractional Diffusion Equations.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/101393/)H. Zhang, F. Liu*, I. Turner and S. Chen (2016) The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/101400/)M. Pan, L. Zheng*, F. Liu, Z. Zhang (2016) Lie group analysis and similarity solution for fractional Blasius flow.

*Communications in Nonlinear Science and Numerical Simulation*. (https://eprints.qut.edu.au/101401/)M. Pan, L. Zheng*, F. Liu, X. Zhang (2016) Modeling heat transport in nanofluids with stagnation point flow using fractional calculus.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/101609/)L. Liu, L. Zheng*, F. Liu, X. Zhang (2016) Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo-Christov flux.

*Communications in Nonlinear Science and Numerical Simulation*. (https://eprints.qut.edu.au/101403/)L. Liu, L. Zheng*, F. Liu and Z. Zhang (2016) An improved heat conduction model with Riesz fractional Cattaneo-Christov flux.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/101616/)S. Qin, F. Liu*, I. Turner, Q. Yu, Q. Yang and V. Vegh (2016) Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2*-weighted magnetic resonance imaging at 7T.

*Magnetic Resonance in Medicine*. (https://eprints.qut.edu.au/94667/)Y. Zhao, Y. Zhang, D. Shi, F. Liu* and I. Turner (2016) Superconvergence Analysis of Nonconforming Finite Element Method for Two-Dimensional Time Fractional Diffusion Equations.

*Applied Mathematics Letters*. (https://eprints.qut.edu.au/101404/)Y. Zhao, Y. Zhang, F. Liu*, I. Turner, Y. Tang and V. Anh (2016) Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/101613/)H. Zhang, F. Liu*, I. Turner and Q. Yang (2016) Numerical solution of the time fractional Black–Scholes model governing European options.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/101611/)L. Feng, P. Zhuang, F. Liu*, I. Turner, J. Li (2016) High-order numerical method for the Riesz space fractional advection-dispersion equation.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/114558/)C. Ming, L. Zheng*, X, Zhang, F. Liu and V. Anh (2016) Flow and heat transfer of power law fluid over a rotating disk with generalized diffusion.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/101608/)P. Zhuang, F. Liu*, I. Turner and V. Anh (2016) Galerkin finite element method and error analysis for the fractional cable equation.

*Numerical Algorithms*. (https://eprints.qut.edu.au/101395/)L. Feng, P. Zhuang, F. Liu*, I. Turner, V. Anh and J. Liu (2016) A fast second-order accurate method for a two-sided space-fractional diffusion equation with variable coefficients.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/101615/)C. Ming, F. Liu*, L. Zheng, I. Turner and V. Anh (2016) Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/101607/)J. Zhao, L. Zheng*, Z. Zhang, F. Liu (2016) Unsteady natural convection boundary layer heat transfer of fractional Maxwell viscoelastic fluid over a vertical plate.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/101405/)J. Zhao, L. Zheng*, X, Zhang, F. Liu (2016) Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects.

*International Journal of Heat and Mass Transfer*. (https://eprints.qut.edu.au/101612/)H. Zhang, F. Liu*, I. Turner, S. Chen and Q. Yang (2016) Numerical simulation of a Finite Moment Log Stable model for a European call option.

*Numerical Algorithms*. (https://eprints.qut.edu.au/103539/)Zhi Cao, Jinhu Zhao, Zhijiang Wang, Liancun Zheng, Fawang Liu (2016) MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid over a moving plate.

*Journal of Molecular Liquids*. (https://eprints.qut.edu.au/101614/)X. Hu, F. Liu*, I. Turner and V. Anh (2016) An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation.

*Numerical Algorithms*. (https://eprints.qut.edu.au/101389/)F. Liu*, P. Zhuang, I. Turner, V. Anh and K. Burrage (2015) A semi-alternating direction method for a 2-D fractional FitzHugh-Nagumo monodomain model on an approximate irregular domain.

*J. Comp Physics*. (https://eprints.qut.edu.au/82648/)M. Zheng, F. Liu*, I. Turner and V. Anh (2015) A novel high order space-time spectral method for the time-fractional Fokker-Planck equation.

*SIAM J. Sci. Computing*. (https://eprints.qut.edu.au/82700/)S. Chen, X. Jiang, F. Liu* and I. Turner (2015) High order unconditionally stable difference schemes for the Riesz space-fractional Telegraph equation.

*Journal of Computational and Applied Mathematics*. (https://eprints.qut.edu.au/82651/)S. Shen, F. Liu*, Q. Liu and V. Anh (2015) Numerical simulation of anomalous infiltration in porous media.

*Numerical Algorithms*. (https://eprints.qut.edu.au/82697/)H. Ye, F. Liu*, V.Anh and I. Turner (2015) Numerical analysis for the time distributed order and Riesz space fractional diffusions on bounded domains.

*IMA Journal of Applied Mathematics*. (https://eprints.qut.edu.au/82691/)L. Feng, P. Zhuang, F. Liu*, I. Turner (2015) Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/82699/)L. Feng, P. Zhuang, F. Liu*, I. Turner and Q. Yang (2015) Second-order approximation for the space fractional diffusion equation with variable coefficient.

*Prog. Frac. Diff. Appl*. (https://eprints.qut.edu.au/114557/)X. Wang, F. Liu*, X. Chen (2015) Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations.

*Advances in Mathematical Physics*. (https://eprints.qut.edu.au/101399/)H. Ye, F. Liu* and V. Anh (2015) Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains.

*J. Comp Physics*. (https://eprints.qut.edu.au/101398/)Q. Yu, V. Vegh, F. Liu*, I. Turner (2015) A variable order fractional differential-based texture enhancement algorithm with application in medical imaging.

*PLOS ONE*. (https://eprints.qut.edu.au/101396/)L. Feng, P. Zhuang, F. Liu*, I. Turner and Y. Gu (2015) Finite element method for space-time fractional diffusion equation.

*Numerical Algorithms*. (https://eprints.qut.edu.au/101394/)Q. Liu, F. Liu*, Y. Gu , P. Zhuang, J. Chen, I. Turner (2015) A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/82350/)X. Hu, H. Liao, F. Liu*, and I. Turner (2015) A center Box method for radially symmetric solution of fractional subdiffusion equation.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/101430/)S. Chen, F. Liu*, X. Jiang , I. Turner and V. Anh (2015) A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/82652/)Zeng, Fanhai, Li, Changpin, Liu, Fawang, Turner, Ian (2015) Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

*SIAM Journal of Scientific Computing*, 37 (1), pp.A55-A78. [eprints.qut.edu.au/82650/]F. Zeng, F. Liu*, C. Li, K. Burrage, I. Turner and V. Anh (2014) Crank-Nicolson ADI spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation.

*SIAM Journal on Numerical Analysis*. (https://eprints.qut.edu.au/82655/)H. Zhang, F. Liu*, P. Zhuang, I. Turner and V. Anh (2014) Numerical analysis of a new space-time variable fractional order advection-dispersion equation.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/88767/)S. Shen, F. Liu*, Q. Liu and V. Anh (2014) Numerical simulation of anomalous infiltration in porous media.

*Numerical Algorithms*. (https://eprints.qut.edu.au/82697/)Q. Yu, , F. Liu*, I. Turner and K. Burrage (2014) Numerical simulation of the fractional Bloch equations.

*Journal of Computational and Applied Mathematics*. (https://eprints.qut.edu.au/77086/)H. Hejazi, T. Moroney and F. Liu (2014) Stability and convergence of a finite volume method for the space fractional advection-dispersion equation.

*Journal of Computational and Applied Mathematics*. (https://eprints.qut.edu.au/56974/)H. Ye, F. Liu*, V. Anh and I. Turner (2014) Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/82658/)Q. Yang, I. Turner, T. Moroney and F. Liu (2014) A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/72905/)Q. Liu, F. Liu*, I. Turner , V. Anh and Y. Gu (2014) A RBF meshless approach for modeling a fractal mobile/immobile transport model.

*Applied Mathematics and Computation*. (https://eprints.qut.edu.au/65162/)S. Chen, F. Liu* and K. Burrage (2014) Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media.

*Computers and Mathematics with Applications*. (https://eprints.qut.edu.au/76879/)S. Shen, F. Liu*, V. Anh, I. Turner, and J. Chen (2014) A novel numerical approximation for the space fractional advection–dispersion equation.

*IMA Journal of Applied Mathematics*. (https://eprints.qut.edu.au/59969/)F. Liu*, P. Zhuang, I. Turner, K. Burrage and V. Anh (2014) A new fractional finite volume method for solving the fractional diffusion equation.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/76835/)J. Song， Q. Yu，F. Liu*, and I. Turner (2014) A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation.

*Numerical Algorithms*. (https://eprints.qut.edu.au/76965/)P. Zhuang, F. Liu*, I. Turner and Y.T. Gu (2014) Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/76865/)J. Chen , F. Liu, Q. Liu , I. Turner, V. Anh , K. Burrage (2014) Numerical simulation for the three- dimension fractional sub-diffusion equation.

*Applied Mathematical Modelling*. (https://eprints.qut.edu.au/101240/)X. Hu, F. Liu*, I. Turner, and V. Anh (2014) A numerical investigation of the time distributed-order diffusion model.

*ANZIAM J.*. (https://eprints.qut.edu.au/114606/)Liu, Fawang, Meerschaert, Mark, McGough, Robert, Zhuang, Pinghui, Liu, Qingxia (2013) Numerical methods for solving the -term time-fractional wave-diffusion equation

*Fractional Calculus and Applied Analysis*, 16 (1), pp.9-25. [eprints.qut.edu.au/76841/]Yu, Qiang, Liu, Fawang, Turner, Ian, Burrage, Kevin (2013) Stability and convergence of an implicit numerical method for the space and time fractional Bloch-Torrey equation

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, 371 (1990), pp.1-18. [eprints.qut.edu.au/77141/]Jiang, H., Liu, Fawang, Meerschaert, Mark, McGough, Robert, Liu, Q. (2013) The fundamental solutions for multi-term modified power law wave equations in a finite domain

*Electronic Journal of Mathematical Analysis and Applications (EJMAA)*, 1 (1), pp.55-66. [eprints.qut.edu.au/113211/]Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo, Chen, Y. (2013) Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

*Numerical Algorithms*, 63 (2), pp.265-290. [eprints.qut.edu.au/60016/]Shen, S., Liu, Fawang, Anh, Vo, Turner, Ian, Chen, J. (2013) A characteristic difference method for the variable-order fractional advection-diffusion equation

*Journal of Applied Mathematics and Computing*, 42 (1 - 2), pp.371-386. [eprints.qut.edu.au/77100/]Zhang, H., Liu, Fawang, Phanikumar, Mantha, Meerschaert, Mark (2013) A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model

*Computers and Mathematics with Applications*, 66 (5), pp.693-701. [eprints.qut.edu.au/76867/]Yu, Qiang, Liu, Fawang, Turner, Ian, Burrage, Kevin (2013) Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

*Open Physics*, 11 (6), pp.646-665. [eprints.qut.edu.au/111581/]Ye, H., Liu, Fawang, Turner, Ian, Anh, Vo, Burrage, Kevin (2013) Series expansion solutions for the -term time and space fractional partial differential equations in two- and three-dimensions

*European Physical Journal: Special Topics*, 222 (8), pp.1901-1914. [eprints.qut.edu.au/77000/]Liu, Fawang, Turner, Ian, Anh, Vo, Yang, Qianqian, Burrage, Kevin (2013) A numerical method for the fractional Fitzhugh–Nagumo monodomain model

*The ANZIAM Journal*, 54, pp.C608-C629. [eprints.qut.edu.au/79808/]Zeng, F., Li, C., Liu, Fawang (2013) High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations

*European Physical Journal: Special Topics*, 222 (8), pp.1885-1900. [eprints.qut.edu.au/77108/]Zeng, Fanhai, Li, Changpin, Liu, Fawang, Turner, Ian (2013) The use of finite difference/element approaches for solving the time-fractional subdiffusion equation

*SIAM Journal of Scientific Computing*, 35 (6), pp.A2976-A3000. [eprints.qut.edu.au/77030/]Chen, Shiping, Liu, Fawang, Turner, Ian, Anh, Vo (2013) An implicit numerical method for the two-dimensional fractional percolation equation

*Applied Mathematics and Computation*, 219 (9), pp.4322-4331. [eprints.qut.edu.au/77313/]Liu, Fawang, Cheng, Shiping, Turner, Ian, Burrage, Kevin, Anh, Vo (2013) Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term

*Open Physics*, 11 (10), pp.1221-1232. [eprints.qut.edu.au/111582/]Chen, Chang-Ming, Liu, Fawang, Burrage, Kevin, Chen, Y. (2013) Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

*IMA Journal of Applied Mathematics*, 78 (5), pp.924-944. [eprints.qut.edu.au/60015/]Chen, J., Liu, Fawang, Burrage, Kevin, Shen, S. (2013) Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

*Journal of Applied Mathematics and Computing*, 41 (1 - 2), pp.33-47. [eprints.qut.edu.au/59964/]Liu, Fawang, Burrage, Kevin, Hamilton, Nicholas (2013) Some novel techniques of parameter estimation for the dynamical models in biological systems

*IMA Journal of Applied Mathematics*, 78 (2), pp.235-260. [eprints.qut.edu.au/45865/]Yu, Q., Liu, F., Turner, I., Burrage, K., Vegh, V. (2012) The use of a Riesz fractional differential-based approach for texture enhancement in image processing

*The 16th Biennial Computational Techniques and Applications Conference*, pp.1-1. [eprints.qut.edu.au/60007/]Hejazi, Hala, Moroney, Timothy, Liu, Fawang, Sun, H, Chen, W, Baleanu, D (2012) A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

*Proceedings of the 5th IFAC Symposium on Fractional Differentiation and Its Applications*, pp.1-6. [eprints.qut.edu.au/51457/]Hejazi, H., Moroney, T., Liu, F. (2012) A comparison of finite difference and finite volume methods
for solving the space fractional advection-dispersion
equation with variable coefficients

*16th Biennial Computational Techniques and Applications Conference*. [eprints.qut.edu.au/60008/]Liu, Fawang, Zhuang, Pinghui, Burrage, Kevin (2012) Numerical methods and analysis for a class of fractional
advection-dispersion models

*Computers and Mathematics with Applications*, 64 (10), pp.2990-3007. [eprints.qut.edu.au/51515/]Jiang, Hui, Liu, Fawang, Turner, Ian, Burrage, Kevin (2012) Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

*Computers and Mathematics with Applications*, 64 (10), pp.3377-3388. [eprints.qut.edu.au/51516/]Shen, Shujun, Liu, Fawang, Chen, Jing, Turner, Ian, Anh, Vo (2012) Numerical techniques for the variable order time fractional diffusion equation

*Applied Mathematics and Computation*, 218 (22), pp.10861-10870. [eprints.qut.edu.au/51509/]Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2012) Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

*Mathematics of Computation*, 81 (277), pp.345-366. [eprints.qut.edu.au/51510/]Li, Changpin, Zeng, Fanhai, Liu, Fawang (2012) Spectral approximations to the fractional integral and derivative

*Fractional Calculus and Applied Analysis*, 15 (3), pp.383-406. [eprints.qut.edu.au/60013/]Chen, J., Liu, Fawang, Anh, Vo, Shen, S., Liu, Q., Liao, C. (2012) The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

*Applied Mathematics and Computation*, 219 (4), pp.1737-1748. [eprints.qut.edu.au/60021/]Yu, Qiang, Liu, Fawang, Turner, Ian, Burrage, Kevin (2012) A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

*Applied Mathematics and Computation*, 219 (8), pp.4082-4095. [eprints.qut.edu.au/60023/]Jiang, Hui, Liu, Fawang, Turner, Ian, Burrage, Kevin (2012) Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

*Journal of Mathematical Analysis and Applications*, 389 (2), pp.1117-1127. [eprints.qut.edu.au/51507/]Zhuang, Pinghui, Gu, YuanTong, Liu, Fawang, Turner, Ian, Yarlagadda, Prasad (2011) Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

*International Journal for Numerical Methods in Engineering*, 88 (13), pp.1346-1362. [eprints.qut.edu.au/45619/]Liu, Fawang, Burrage, Kevin (2011) Novel techniques in parameter estimation for fractional dynamical models arising from biological systems

*Computers and Mathematics with Applications*, 62 (3), pp.822-833. [eprints.qut.edu.au/52468/]Yang, Qianqian, Turner, Ian, Liu, Fawang, Ilic, Milos (2011) Novel numerical methods for solving the time-space fractional diffusion equation in 2D

*SIAM Journal of Scientific Computing*, 33 (3), pp.1159-1180. [eprints.qut.edu.au/40662/]Liu, Q., Liu, Fawang, Turner, Ian, Anh, Vo (2011) Finite element approximation for a modified anomalous subdiffusion equation

*Applied Mathematical Modelling*, 35 (8), pp.4103-4116. [eprints.qut.edu.au/52255/]Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo (2011) Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid

*Computers and Mathematics with Applications*, 62 (3), pp.971-986. [eprints.qut.edu.au/52621/]Shen, Shujun, Liu, Fawang, Anh, Vo (2011) Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation

*Numerical Algorithms*, 56 (3), pp.383-403. [eprints.qut.edu.au/42736/]Chen, Shiping, Liu, Fawang, Anh, Vo (2011) A novel implicit finite difference method for the one-dimensional fractional percolation equation

*Numerical Algorithms*, 56 (4), pp.517-535. [eprints.qut.edu.au/43080/]Liu, Q., Gu, YuanTong, Zhuang, Pinghui, Liu, Fawang, Nie, Yufeng (2011) An implicit RBF meshless approach for time fractional diffusion equations

*Computational Mechanics*, 48 (1), pp.1-12. [eprints.qut.edu.au/45681/]Liu, Fawang, Yang, Qianqian, Turner, Ian (2011) Two new implicit numerical methods for the fractional cable equation

*Journal of Computational and Nonlinear Dynamics*, 6 (1), pp.1-7. [eprints.qut.edu.au/37944/]Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2011) Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

*Applied Mathematics and Computation*, 217 (12), pp.5729-5742. [eprints.qut.edu.au/42692/]Yang, Qianqian, Moroney, Timothy, Burrage, Kevin, Turner, Ian, Liu, Fawang, McLean, W, Roberts, T (2011) Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

*The ANZIAM Journal, Volume 52, Electronic Supplement: Proceedings of the 15th Biennial Computational Techniques and Applications Conference*, pp.C395-C409. [eprints.qut.edu.au/46269/]Chen, Chang-Ming, Liu, Fawang, Burrage, Kevin (2011) Numerical analysis for a variable-order nonlinear cable equation

*Journal of Computational and Applied Mathematics*, 236 (2), pp.209-224. [eprints.qut.edu.au/45864/]Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2010) Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equations

*SIAM Journal on Computing*, 32 (4), pp.1740-1760. [eprints.qut.edu.au/42998/]Ilic, Milos, Turner, Ian, Liu, Fawang, Anh, Vo (2010) Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium

*Applied Mathematics and Computation*, 216 (8), pp.2248-2262. [eprints.qut.edu.au/42795/]Zhang, H., Liu, Fawang, Anh, Vo (2010) Galerkin finite element approximation of symmetric space-fractional partial differential equations

*Applied Mathematics and Computation*, 217 (6), pp.2534-2545. [eprints.qut.edu.au/43293/]Yang, Qianqian, Liu, Fawang, Turner, Ian (2010) Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

*Applied Mathematical Modelling*, 34 (1), pp.200-218. [eprints.qut.edu.au/29844/]Q. Yang, F. Liu* and I. Turner (2010) Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.

*International Journal of Differential Equations*. (doi:10.1155/2010/464321)Y. Gu, P. Zhuang and F. Liu (2010) An Advanced Implicit Meshless Approach for the Non-linear Anomalous Subdiffusion Equation.

*Computer Modeling in Engineering & Sciences*. (doi: 10.3970/cmes.2010.056.303.)Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo (2010) Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

*Numerical Algorithms*, 54 (1), pp.1-21. [eprints.qut.edu.au/29756/]Liu, Fawang, Burrage, Kevin, Chen, Podlubny, I, Vinagre Jara, B M, Feliu Batlle, V, Tejado Balsera, I (2010) Parameter estimation for fractional dynamical models in biological systems

*Proceedings of the 4th IFAC Workshop on Fractional Differentiation and Its Applications*, pp.1-8. [eprints.qut.edu.au/80414/]Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

*SIAM Journal on Numerical Analysis*, 47 (3), pp.1760-1781. [eprints.qut.edu.au/29755/]Liu, Fawang, Yang, Chen, Burrage, Kevin (2009) Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

*Journal of Computational and Applied Mathematics*, 231 (1), pp.160-176. [eprints.qut.edu.au/29754/]Yang, Qianqian, Turner, Ian, Liu, Fawang (2009) Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

*Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM)*, 50, pp.C800-C814. [eprints.qut.edu.au/37852/]Q. Yang, F. Liu*, I. Turner (2009) Computationally efficient numerical methods for time and space fractional Fokker-Planck equations.

*Physica Scripta*.Lin, R, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

*Applied Mathematics and Computation*, 212 (2), pp.435-445. [eprints.qut.edu.au/29758/]Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

*IMA Journal of Applied Mathematics*, 74 (5), pp.645-667. [eprints.qut.edu.au/29759/]Liu, Q, Liu, Fawang, Turner, Ian, Anh, Vo (2009) Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

*IMA Journal of Applied Mathematics*, 74 (2), pp.201-229. [eprints.qut.edu.au/29757/]Chen, S, Liu, Fawang, Zhuang, Pinghui, Anh, Vo (2009) Finite difference approximations for the fractional Fokker–Planck equation

*Applied Mathematical Modelling*, 33 (1), pp.256-273. [eprints.qut.edu.au/14804/]Yu, Q, Song, J, Liu, Fawang, Anh, Vo, Turner, Ian (2009) An approximate solution for the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model using the Adomian decomposition method

*Journal of Algorithms and Computational Technology*, 3 (4), pp.553-571. [eprints.qut.edu.au/42823/]Chen, Chang-Ming, Liu, Fawang, Anh, Vo (2009) A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative

*Journal of Computational and Applied Mathematics*, 223 (2), pp.777-789. [eprints.qut.edu.au/30935/]Chen, Chang-Ming, Liu, Fawang (2009) A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation

*Journal of Applied Mathematics and Computing*, 30 (1-2), pp.219-236. [eprints.qut.edu.au/30766/]Q. Liu and F. Liu (2009) Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives in uniform media.

*Mathematica Numerica Numerica Sinica*.Chen, S, Liu, Fawang (2008) ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation

*Journal of Applied Mathematics and Computing*, 26 (1-2), pp.295-311. [eprints.qut.edu.au/30771/]Y. Lin and F. Liu (2008) Analytical Solution for the nonhomogeneous anomalous subdiffusion equation.

*Journal of Xiamen University*.Shen, Shujun, Liu, Fawang, Anh, Vo (2008) Fundamental solution and discrete random walk model for time-space fractional diffusion equation

*Journal of Applied Mathematics and Computing*, 28 (1-2), pp.147-164. [eprints.qut.edu.au/30922/]Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2008) New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation

*SIAM Journal on Numerical Analysis*, 46 (2), pp.1079-1095. [eprints.qut.edu.au/30905/]Zhang, Hong-Mei, Liu, Fawang (2008) Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

*Journal of Applied Mathematics and Computing*, 26 (1-2), pp.1-14. [eprints.qut.edu.au/30897/]Chen, Chang-Ming, Liu, Fawang, Anh, Vo (2008) Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives

*Applied Mathematics and Computation*, 204, pp.340-351. [eprints.qut.edu.au/30842/]S. Shen and F. Liu (2008) A Computationally Efficient Solution Method for a Riesz Space Fractional Advection-Dispersion Equation.

*Journal of Xiamen University*.Shen, S, Liu, Fawang, Anh, Vo, Turner, Ian (2008) The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation

*IMA Journal of Applied Mathematics*, 73, pp.850-872. [eprints.qut.edu.au/30652/]Yu, Q, Liu, Fawang, Anh, Vo, Turner, Ian (2008) Solving linear and non-linear space-time fractional reaction-diffusion equations by the adomian decomposition method

*International Journal for Numerical Methods in Engineering*, 74 (1), pp.138-158. [eprints.qut.edu.au/43102/]Chen, Jing, Liu, Fawang, Anh, Vo (2008) Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables

*Journal of Mathematical Analysis and Applications*, 338 (2), pp.1364-1377. [eprints.qut.edu.au/43041/]Huang, F, Liu, Fawang (2008) The time fractional diffusion and wave equations in an n-dimensional half space with mixed boundary conditions

*Pacific Journal of Applied Mathematics*, 1 (4), pp.67-77. [eprints.qut.edu.au/30795/]J. Chen, F. Liu*, I. Turner and V. Anh (2008) The fundamental and numerical solutions of the Riesz space fractional reaction-dispersion equation.

*ANZIAM J.*.H. Zhang and F. Liu (2008) The solution of a special form of the time fractional Navier-Stokes equations.

*Chinese Journal of Engineering Mathematics*.Chen, Chang-ming, Liu, Fawang, Burrage, Kevin (2008) Finite difference methods and a fourier analysis for the fractional reaction–subdiffusion equation

*Applied Mathematics and Computation*, 198 (2), pp.754-769. [eprints.qut.edu.au/14755/]Chen, Chang-ming, Liu, Fawang, Turner, Ian, Anh, Vo (2007) A Fourier method for the fractional diffusion equation describing sub-diffusion

*Journal of Computational Physics*, 227 (2), pp.886-897. [eprints.qut.edu.au/14739/]Zhuang, Pinghui, Liu, Fawang (2007) Implicit difference approximation for the two-dimensional space-time fractional diffusion equation

*Journal of Applied Mathematics and Computing*, 25 (1-2), pp.269-282. [eprints.qut.edu.au/14892/]Zhang, H, Liu, Fawang, Anh, Vo (2007) Numerical approximation of Levy–Feller diffusion equation and its probability interpretation

*Journal of Computational and Applied Mathematics*, 206 (2), pp.1098-1115. [eprints.qut.edu.au/10482/]Liu, Q, Liu, Fawang, Turner, Ian, Anh, Vo (2007) Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method

*Journal of Computational Physics*, 222 (1), pp.57-70. [eprints.qut.edu.au/10478/]Zhuang, Pinghui, Liu, Fawang (2007) Finite difference approximation for two-dimensional time fractional diffusion equation

*Journal of Algorithms and Computational Technology*, 1 (1), pp.1-15. [eprints.qut.edu.au/15085/]Cai, Xin, Liu, Fawang (2007) Numerical simulation of the fractional-order control system

*Journal of Applied Mathematics and Computing*, 23 (1-2), pp.229-241. [eprints.qut.edu.au/14891/]Lin, R, Liu, Fawang (2007) Fractional High Order Methods For The Nonlinear Fractional Ordinary Differential Equation

*Nonlinear Analysis: Modelling and Control*, 66 (4), pp.856-869. [eprints.qut.edu.au/21852/]Liu, Fawang, Zhuang, Pinghui, Anh, Vo, Turner, Ian, Burrage, Kevin (2007) Stability and convergence next term of the difference methods for the space-time fractional advection-diffusion equation

*Applied Mathematics and Computation*, 191 (1), pp.12-20. [eprints.qut.edu.au/44379/]Chen, Chang-ming, Liu, Fawang, Turner, Ian, Anh, Vo (2007) Implicit Difference Approximation of the Galilei Invariant Fractional Advection Diffusion Equation

*The ANZIAM Journal*, 48 (Supp), pp.Article number: CTAC 775-789. [eprints.qut.edu.au/43145/]H. Zhang and F. Liu (2007) A solution technique of the time-fractional telegraph equation.

*Journal of Xiamen University*.C. Yin and F. Liu (2007) Some techniques for solving the fractional differential Equations of Endolymph.

*Journal of Xiamen University*.X. Zhang and F. Liu (2007) Analytical solution of one dimensional fractional diffusion-wave equation under mixed boundary conditions.

*Journal of Fuzhou University*.X. Wang and F. Liu (2007) Separation of Variables Method for fractional diffusion-wave equation with initial-boundary value problem in three dimension.

*Journal of Fuzhou University*.H. Zhang and F. Liu (2007) Super linear convergence approximation of the space fractional diffusion equation.

*Journal of Xiamen University*.Chen, Jing, Liu, Fawang (2007) Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation

*Numerical Mathematics*, 16 (3), pp.253-264. [eprints.qut.edu.au/43015/]X. Cai and F. Liu (2007) A high order implicit method for the Riesz space fractional diffusion equation.

*Journal of Xiamen University*.J. Song, F. Liu and P. ,Zhuang (2007) An approximate solution for the non-linear anomalous subdiffusion equation using the Adomian decomposition method.

*Journal of Xiamen University*.Zhang, Hongmei, Liu, Fawang (2007) The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions

*Numerical Mathematics*, 16 (2), pp.181-192. [eprints.qut.edu.au/42817/]Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2007) Numerical Treatment For The Fractional Fokker-Planck Equation

*The ANZIAM Journal*, 48 (Supp), pp.Article number: CTAC 759-774. [eprints.qut.edu.au/43101/]Y. Lin, P. Zhuang and F. Liu (2007) Fractional high order approximation for the system of the nonlinear fractional ordinary differential equations.

*Journal of Xiamen University*.Yin, Cui-ying, Liu, Fawang, Anh, Vo (2007) Numerical simulation of the nonlinear fractional dynamical systems with fractional damping for the extensible and inextensible pendulum

*Journal of Algorithms and Computational Technology*, 1 (4), pp.427-447. [eprints.qut.edu.au/15090/]Zhuang, Pinghui, Liu, Fawang (2006) Implicit difference approximation for the time fractional diffusion equation

*Journal of Applied Mathematics and Computing*, 22 (3), pp.87-99. [eprints.qut.edu.au/23700/]Ilic, Milos, Liu, Fawang, Turner, Ian, Anh, Vo (2006) Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

*Fractional Calculus and Applied Analysis*, 9 (4), pp.333-349. [eprints.qut.edu.au/23835/]Liu, Fawang, Zhuang, P, Anh, Vo, Turner, Ian, Blyth, B, Stacey, A, Shepherd, J (2006) A fractional-order implicit difference approximation for the space-time fractional diffusion equation

*Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference (ANZIAM Journal, Vol 47)*, pp.48-68. [eprints.qut.edu.au/25774/]Yang, C, Liu, Fawang, Blyth, B, Stacey, A, Shepherd, J (2006) A Computationally Effective Predictor-Corrector Method for Simulating Fractional Order Dynamical Control System

*Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference (ANZIAM Journal, Vol 47)*, pp.168-184. [eprints.qut.edu.au/24122/]Q. Liu and F. Liu (2006) Lévy -Feller advection-diffusion equation.

*Journal of Xiamen University*.Q. Yu and F. Liu (2006) Implicit difference approximation for the time-fractional order reaction-diffusion equation.

*Journal of Xiamen University*.Shen, Shujun, Liu, Fawang, Anh, Vo, Turner, Ian (2006) Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

*Journal of Applied Mathematics and Computing*, 22 (3), pp.1-19. [eprints.qut.edu.au/23024/]Liu, Fawang, Anh, Vo, Turner, Ian, Bajracharya, Kiran, Huxley, W, Ninghu, Ninghu (2006) A finite volume simulation model for saturated–unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia

*Applied Mathematical Modelling*, 30 (4), pp.352-366. [eprints.qut.edu.au/10479/]Huang, Fenghui, Liu, Fawang (2005) The Fundamental Solution of the Space-Time Fractional Advection-Dispersion Equation

*Journal of Applied Mathematics and Computing*, 18 (1 - 2), pp.339-350. [eprints.qut.edu.au/23460/]Huang, Fenghui, Liu, Fawang (2005) The Space-Time Fractional Diffusion Equation with Caputo Derivatives

*Journal of Applied Mathematics and Computing*, 19 (1 - 2), pp.179-190. [eprints.qut.edu.au/21880/]Huang, F, Liu, Fawang (2005) The Time Fractional Diffusion Equation and the Advection-Dispersion Equation

*The ANZIAM Journal*, 46, pp.317-330. [eprints.qut.edu.au/23432/]Shen, S, Liu, Fawang, May, R (2005) Error analysis of an explicit finite difference approximation for the space fractional diffusion equation with insulated ends

*Proceedings of the 2004 International Conference on Computational Techniques and Applications*, pp.872-887. [eprints.qut.edu.au/25299/]M. Ilic, F. Liu*, I. Turner and V. Anh (2005) Numerical approximation of a fractional-in-space diffusion equation (I).

*Fractional Calculus and Applied Analysis*.X. Lu and F. Liu (2005) Time Fractional Diffusion-Reaction Equation.

*Numerical Mathematics: A Journal of Chinese Universities*.C. Yang and F. Liu (2005) A fractional Predictor-Corrector method of the fractional Relaxation-Oscillation equation.

*Journal of Xiamen University*.P. Zhuang and F. Liu (2005) An explicit difference approximation for the space-time fractional diffusion equation.

*Numerical Mathematics: A Journal of Chinese Universities*.Su, Ninghu, Sander, G, Liu, Fawang, Anh, Vo, Barry, D (2005) Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity

*Applied Mathematical Modelling*, 29 (9), pp.852-870. [eprints.qut.edu.au/22531/]Liu, Fawang, Shen, S, Anh, Vo, Turner, Ian (2004) Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation

*The ANZIAM Journal*, 46 (5), pp.C488-C504. [eprints.qut.edu.au/22160/]Liu, Fawang, Anh, Vo, Turner, Ian (2004) Numerical solution of the space fractional Fokker-Planck equation

*Journal of Computational and Applied Mathematics*, 166, pp.209-219. [eprints.qut.edu.au/10113/]Liu, Fawang, Anh, Vo, Turner, Ian, Zhuang, P (2004) Numerical simulation for solute transport in fractal porous media

*The ANZIAM Journal*, 45, pp.461-473. [eprints.qut.edu.au/22238/]R. Lin and F. Liu (2004) A high order approximation of fractional order ordinary differential equation initial value problem.

*Journal of Xiamen University*.S. Shen and F. Liu (2004) A computational effective method for fractional order Bagley-Torvik equation.

*Journal of Xiamen University*.X. Lu and F. Liu (2004) The explicit and implicit finite difference approximations for a space fractional advection diffusion equation.

*Computational Mechanics*.S. Shen and F. Liu (2004) A fully discrete difference approximation for the time fractional diffusion equation.

*Computational Mechanics*.R. Lin and F. Liu (2004) Analysis of fractional-order numerical method for the fractional relaxation equation.

*Computational Mechanics*.Liu, Fawang, Anh, Vo, Turner, Ian, Zhuang, P (2003) Time fractional advection-dispersion equation

*Journal of Applied Mathematics and Computing*, 13 (1-2), pp.233-245. [eprints.qut.edu.au/22919/]## Conference Papers

F. Liu*, I. Turner and K. Burrage (2015) Computationally efficient numerical techniques for a space-fractional FitzHugh-Nagumo monodomain model.

*ICCES15, Tech. Science Press, (2015)*.F. Liu*, P. Zhuang, I. Turner, V. Anh and K. Burrage (2014) Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model.

*IEEE Explore Conference Proceedings, Italy*. (https://eprints.qut.edu.au/84638/)Q. Yang, F. Liu* and I. Turner (2008) Numerical solution techniques for time-space fractional Fokker-Planck equations.

*The Proceedings of the 3rd IFAC Workshop on Fractional Differentiation and its Applications, Ankara, Turkey*.## Books

F. Liu*, P. Zhuang and Q. Liu (2015) Numerical Methods of Fractional Partial Differential Equations and Applications.

*Science Press, China, (in Chinese), November 2015，ISBN 978-7-03-046335-7*. (https://eprints.qut.edu.au/101829/)## Thesis

Shanlin Qin (2017) Fractional order models: Numerical simulation and application to medical imaging.

*Queensland University of Technology*. (https://eprints.qut.edu.au/115108/)Qiang Yu (2013) Numerical simulation of anomalous diffusion with application to medical imaging.

*Queensland University of Technology*. (https://eprints.qut.edu.au/62068/)Qianqian Yang (2010) Novel analytical and numerical methods for solving fractional dynamical system.

*Queensland University of Technology*. (https://eprints.qut.edu.au/35750/)Feng, Libo (2019) Numerical investigation and application of fractional dynamical systems [eprints.qut.edu.au/126980/]