**Journal Articles**

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*, 80,(2), pp.533-555. (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*, 352, pp.437-452. (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*, 70, pp.354-371. (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*, 136, pp.139-151. (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*, 345, pp.515-534. (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*, 95, pp.143-149. (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*, 73, pp.615-636. (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*, 35, pp.875-893. (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*, 356, pp.1-12. (https://www.sciencedirect.com/science/article/pii/S0096300319301894)

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*, 56, pp.270-286. (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*, 120, pp.1132-1145. (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*, 75, pp.965-980. (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*, 336, pp.114-126. (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*, 79, pp.92-99. (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*, 77, pp.114-121. (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*, 326, pp.108-116. (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)

*Applied Mathematics and Computation*, *338*, pp. 290-304. (https://eprints.qut.edu.au/121061/)

*Applied Numerical Mathematics*, *134*, pp. 66-80. (https://eprints.qut.edu.au/120143/)

*Applied Mathematics and Computation*, *339*, pp. 186-198. (https://eprints.qut.edu.au/121063/)

*Computers and Mathematics with Applications*, *76*(10), pp. 2460-2476. (https://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*, 79,(1), pp.19-40 . (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*, 36,(4), pp.563-578.

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 *, 140,(9), pp.091701.

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*, 76, pp.245-256. (https://www.sciencedirect.com/science/article/pii/S0898122118302141)

*International Journal of Heat and Mass Transfer*, *127*(Part B), pp. 165-172. (https://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 *, 21,(4), pp.1073-1103. (https://www.degruyter.com/view/j/fca.2018.21.issue-4/fca-2018-0058/fca-2018-0058.xml)

*Journal of Computational Physics*, *338*, pp. 493-510. (https://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/)

*SIAM Journal of Scientific Computing*, *37*(1), A55-A78. (https://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/)

*Fractional Calculus and Applied Analysis*, *16*(1), pp. 9-25. (https://eprints.qut.edu.au/76841/)

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, *371*(1990), pp. 1-18. (https://eprints.qut.edu.au/77141/)

*Electronic Journal of Mathematical Analysis and Applications (EJMAA)*, *1*(1), pp. 55-66. (https://eprints.qut.edu.au/113211/)

*Numerical Algorithms*, *63*(2), pp. 265-290. (https://eprints.qut.edu.au/60016/)

*Journal of Applied Mathematics and Computing*, *42*(1 - 2), pp. 371-386. (https://eprints.qut.edu.au/77100/)

*Computers and Mathematics with Applications*, *66*(5), pp. 693-701. (https://eprints.qut.edu.au/76867/)

*Open Physics*, *11*(6), pp. 646-665. (https://eprints.qut.edu.au/111581/)

*European Physical Journal: Special Topics*, *222*(8), pp. 1901-1914. (https://eprints.qut.edu.au/77000/)

*The ANZIAM Journal*, *54*, C608-C629. (https://eprints.qut.edu.au/79808/)

*European Physical Journal: Special Topics*, *222*(8), pp. 1885-1900. (https://eprints.qut.edu.au/77108/)

*SIAM Journal of Scientific Computing*, *35*(6), A2976-A3000. (https://eprints.qut.edu.au/77030/)

*Applied Mathematics and Computation*, *219*(9), pp. 4322-4331. (https://eprints.qut.edu.au/77313/)

*Open Physics*, *11*(10), pp. 1221-1232. (https://eprints.qut.edu.au/111582/)

*IMA Journal of Applied Mathematics*, *78*(5), pp. 924-944. (https://eprints.qut.edu.au/60015/)

*Journal of Applied Mathematics and Computing*, *41*(1 - 2), pp. 33-47. (https://eprints.qut.edu.au/59964/)

*IMA Journal of Applied Mathematics*, *78*(2), pp. 235-260. (https://eprints.qut.edu.au/45865/)

*The 16th Biennial Computational Techniques and Applications Conference*, 2012-09-23 - 2012-09-26. (https://eprints.qut.edu.au/60007/)

*Proceedings of the 5th IFAC Symposium on Fractional Differentiation and Its Applications.* Hohai University, China, pp. 1-6. (https://eprints.qut.edu.au/51457/)

*16th Biennial Computational Techniques and Applications Conference*, 2012-09-23 - 2012-09-26. (https://eprints.qut.edu.au/60008/)

*Computers and Mathematics with Applications*, *64*(10), pp. 2990-3007. (https://eprints.qut.edu.au/51515/)

*Computers and Mathematics with Applications*, *64*(10), pp. 3377-3388. (https://eprints.qut.edu.au/51516/)

*Applied Mathematics and Computation*, *218*(22), pp. 10861-10870. (https://eprints.qut.edu.au/51509/)

*Mathematics of Computation*, *81*(277), pp. 345-366. (https://eprints.qut.edu.au/51510/)

*Fractional Calculus and Applied Analysis*, *15*(3), pp. 383-406. (https://eprints.qut.edu.au/60013/)

*Applied Mathematics and Computation*, *219*(4), pp. 1737-1748. (https://eprints.qut.edu.au/60021/)

*Applied Mathematics and Computation*, *219*(8), pp. 4082-4095. (https://eprints.qut.edu.au/60023/)

*Journal of Mathematical Analysis and Applications*, *389*(2), pp. 1117-1127. (https://eprints.qut.edu.au/51507/)

*International Journal for Numerical Methods in Engineering*, *88*(13), pp. 1346-1362. (https://eprints.qut.edu.au/45619/)

*Computers and Mathematics with Applications*, *62*(3), pp. 822-833. (https://eprints.qut.edu.au/52468/)

*SIAM Journal of Scientific Computing*, *33*(3), pp. 1159-1180. (https://eprints.qut.edu.au/40662/)

*Applied Mathematical Modelling*, *35*(8), pp. 4103-4116. (https://eprints.qut.edu.au/52255/)

*Computers and Mathematics with Applications*, *62*(3), pp. 971-986. (https://eprints.qut.edu.au/52621/)

*Numerical Algorithms*, *56*(3), pp. 383-403. (https://eprints.qut.edu.au/42736/)

*Numerical Algorithms*, *56*(4), pp. 517-535. (https://eprints.qut.edu.au/43080/)

*Computational Mechanics*, *48*(1), pp. 1-12. (https://eprints.qut.edu.au/45681/)

*Journal of Computational and Nonlinear Dynamics*, *6*(1), pp. 1-7. (https://eprints.qut.edu.au/37944/)

*Applied Mathematics and Computation*, *217*(12), pp. 5729-5742. (https://eprints.qut.edu.au/42692/)

*The ANZIAM Journal, Volume 52, Electronic Supplement: Proceedings of the 15th Biennial Computational Techniques and Applications Conference.* Cambridge University Press, United Kingdom, C395-C409. (https://eprints.qut.edu.au/46269/)

*Journal of Computational and Applied Mathematics*, *236*(2), pp. 209-224. (https://eprints.qut.edu.au/45864/)

*SIAM Journal on Computing*, *32*(4), pp. 1740-1760. (https://eprints.qut.edu.au/42998/)

*Applied Mathematics and Computation*, *216*(8), pp. 2248-2262. (https://eprints.qut.edu.au/42795/)

*Applied Mathematics and Computation*, *217*(6), pp. 2534-2545. (https://eprints.qut.edu.au/43293/)

*Applied Mathematical Modelling*, *34*(1), pp. 200-218. (https://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*, 56,(3), pp.303-334. (doi: 10.3970/cmes.2010.056.303.)

*Numerical Algorithms*, *54*(1), pp. 1-21. (https://eprints.qut.edu.au/29756/)

*Proceedings of the 4th IFAC Workshop on Fractional Differentiation and Its Applications.* Technical University of Kosice, University of Extremadura, Spain, pp. 1-8. (https://eprints.qut.edu.au/80414/)

*SIAM Journal on Numerical Analysis*, *47*(3), pp. 1760-1781. (https://eprints.qut.edu.au/29755/)

*Journal of Computational and Applied Mathematics*, *231*(1), pp. 160-176. (https://eprints.qut.edu.au/29754/)

*Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM)*, *50*, C800-C814. (https://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*, 136, pp.1-7.

*Applied Mathematics and Computation*, *212*(2), pp. 435-445. (https://eprints.qut.edu.au/29758/)

*IMA Journal of Applied Mathematics*, *74*(5), pp. 645-667. (https://eprints.qut.edu.au/29759/)

*IMA Journal of Applied Mathematics*, *74*(2), pp. 201-229. (https://eprints.qut.edu.au/29757/)

*Applied Mathematical Modelling*, *33*(1), pp. 256-273. (https://eprints.qut.edu.au/14804/)

*Journal of Algorithms and Computational Technology*, *3*(4), pp. 553-571. (https://eprints.qut.edu.au/42823/)

*Journal of Computational and Applied Mathematics*, *223*(2), pp. 777-789. (https://eprints.qut.edu.au/30935/)

*Journal of Applied Mathematics and Computing*, *30*(1-2), pp. 219-236. (https://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*, 31,(2), pp.179-194.

*Journal of Applied Mathematics and Computing*, *26*(1-2), pp. 295-311. (https://eprints.qut.edu.au/30771/)

Y. Lin and F. Liu (2008) Analytical Solution for the nonhomogeneous anomalous subdiffusion equation. *Journal of Xiamen University*, 47,(2), pp.158-163.

*Journal of Applied Mathematics and Computing*, *28*(1-2), pp. 147-164. (https://eprints.qut.edu.au/30922/)

*SIAM Journal on Numerical Analysis*, *46*(2), pp. 1079-1095. (https://eprints.qut.edu.au/30905/)

*Journal of Applied Mathematics and Computing*, *26*(1-2), pp. 1-14. (https://eprints.qut.edu.au/30897/)

*Applied Mathematics and Computation*, *204*, pp. 340-351. (https://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*, 47,(1), pp.20-24.

*IMA Journal of Applied Mathematics*, *73*, pp. 850-872. (https://eprints.qut.edu.au/30652/)

*International Journal for Numerical Methods in Engineering*, *74*(1), pp. 138-158. (https://eprints.qut.edu.au/43102/)

*Journal of Mathematical Analysis and Applications*, *338*(2), pp. 1364-1377. (https://eprints.qut.edu.au/43041/)

*Pacific Journal of Applied Mathematics*, *1*(4), pp. 67-77. (https://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.*(50), pp.45-57.

H. Zhang and F. Liu (2008) The solution of a special form of the time fractional Navier-Stokes equations. *Chinese Journal of Engineering Mathematics*, 25,(5), pp.935-938 .

*Applied Mathematics and Computation*, *198*(2), pp. 754-769. (https://eprints.qut.edu.au/14755/)

*Journal of Computational Physics*, *227*(2), pp. 886-897. (https://eprints.qut.edu.au/14739/)

*Journal of Applied Mathematics and Computing*, *25*(1-2), pp. 269-282. (https://eprints.qut.edu.au/14892/)

*Journal of Computational and Applied Mathematics*, *206*(2), pp. 1098-1115. (https://eprints.qut.edu.au/10482/)

*Journal of Computational Physics*, *222*(1), pp. 57-70. (https://eprints.qut.edu.au/10478/)

*Journal of Algorithms and Computational Technology*, *1*(1), pp. 1-15. (https://eprints.qut.edu.au/15085/)

*Journal of Applied Mathematics and Computing*, *23*(1-2), pp. 229-241. (https://eprints.qut.edu.au/14891/)

*Nonlinear Analysis: Modelling and Control*, *66*(4), pp. 856-869. (https://eprints.qut.edu.au/21852/)

*Applied Mathematics and Computation*, *191*(1), pp. 12-20. (https://eprints.qut.edu.au/44379/)

*The ANZIAM Journal*, *48*(Supp), Article number: CTAC 775-789. (https://eprints.qut.edu.au/43145/)

H. Zhang and F. Liu (2007) A solution technique of the time-fractional telegraph equation. *Journal of Xiamen University*, 46,(1), pp.10-13.

C. Yin and F. Liu (2007) Some techniques for solving the fractional differential Equations of Endolymph. *Journal of Xiamen University*, 46,(2), pp.170-174.

X. Zhang and F. Liu (2007) Analytical solution of one dimensional fractional diffusion-wave equation under mixed boundary conditions. *Journal of Fuzhou University *, 35,(4), pp.1-5.

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*, 35,(4), pp.520-525.

H. Zhang and F. Liu (2007) Super linear convergence approximation of the space fractional diffusion equation. *Journal of Xiamen University*, 46,(4), pp.464-468.

*Numerical Mathematics*, *16*(3), pp. 253-264. (https://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*, 46,(3), pp.317-321.

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*, 46,(4), pp.469-473.

*Numerical Mathematics*, *16*(2), pp. 181-192. (https://eprints.qut.edu.au/42817/)

*The ANZIAM Journal*, *48*(Supp), Article number: CTAC 759-774. (https://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*, 46, pp.765-769.

*Journal of Algorithms and Computational Technology*, *1*(4), pp. 427-447. (https://eprints.qut.edu.au/15090/)

*Journal of Applied Mathematics and Computing*, *22*(3), pp. 87-99. (https://eprints.qut.edu.au/23700/)

*Fractional Calculus and Applied Analysis*, *9*(4), pp. 333-349. (https://eprints.qut.edu.au/23835/)

*Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference (ANZIAM Journal, Vol 47).* ANZIAM Journal, Australia, pp. 48-68. (https://eprints.qut.edu.au/25774/)

*Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference (ANZIAM Journal, Vol 47).* ANZIAM Journal, Australia, pp. 168-184. (https://eprints.qut.edu.au/24122/)

Q. Liu and F. Liu (2006) Lévy -Feller advection-diffusion equation. *Journal of Xiamen University*, 45,(2), pp.171-174.

Q. Yu and F. Liu (2006) Implicit difference approximation for the time-fractional order reaction-diffusion equation. *Journal of Xiamen University*, 45,(3), pp.315-319 .

*Journal of Applied Mathematics and Computing*, *22*(3), pp. 1-19. (https://eprints.qut.edu.au/23024/)

*Applied Mathematical Modelling*, *30*(4), pp. 352-366. (https://eprints.qut.edu.au/10479/)

*Journal of Applied Mathematics and Computing*, *18*(1 - 2), pp. 339-350. (https://eprints.qut.edu.au/23460/)

*Journal of Applied Mathematics and Computing*, *19*(1 - 2), pp. 179-190. (https://eprints.qut.edu.au/21880/)

*The ANZIAM Journal*, *46*, pp. 317-330. (https://eprints.qut.edu.au/23432/)

*Proceedings of the 2004 International Conference on Computational Techniques and Applications.* Australian Mathematical Society, Australia, pp. 872-887. (https://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*, 8,(3), pp.323-341.

X. Lu and F. Liu (2005) Time Fractional Diffusion-Reaction Equation. *Numerical Mathematics: A Journal of Chinese Universities*, 27,(3), pp.267-273.

C. Yang and F. Liu (2005) A fractional Predictor-Corrector method of the fractional Relaxation-Oscillation equation. *Journal of Xiamen University*, 44,(6), pp.761-765 .

P. Zhuang and F. Liu (2005) An explicit difference approximation for the space-time fractional diffusion equation. *Numerical Mathematics: A Journal of Chinese Universities*, 27, pp.223-230.

*Applied Mathematical Modelling*, *29*(9), pp. 852-870. (https://eprints.qut.edu.au/22531/)

*The ANZIAM Journal*, *46*(5), C488-C504. (https://eprints.qut.edu.au/22160/)

*Journal of Computational and Applied Mathematics*, *166*, pp. 209-219. (https://eprints.qut.edu.au/10113/)

*The ANZIAM Journal*, *45*, pp. 461-473. (https://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*, 43,(1), pp.25-30.

S. Shen and F. Liu (2004) A computational effective method for fractional order Bagley-Torvik equation. *Journal of Xiamen University*, 45,(3), pp.306-311.

X. Lu and F. Liu (2004) The explicit and implicit finite difference approximations for a space fractional advection diffusion equation. *Computational Mechanics*, ID-120.

S. Shen and F. Liu (2004) A fully discrete difference approximation for the time fractional diffusion equation. *Computational Mechanics*, ID-79.

R. Lin and F. Liu (2004) Analysis of fractional-order numerical method for the fractional relaxation equation. *Computational Mechanics*, ID-362.

*Journal of Applied Mathematics and Computing*, *13*(1-2), pp. 233-245. (https://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/)

*Numerical investigation and application of fractional dynamical systems.* PhD by Publication, Queensland University of Technology. (https://eprints.qut.edu.au/126980/)