# Publications

## 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)

Shi, Z., Zhao, Y., , 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. (https://eprints.qut.edu.au/121061/)

Chen, S., , , & (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. (https://eprints.qut.edu.au/120143/)

Zhang, H., , Chen, S., , & 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. (https://eprints.qut.edu.au/121063/)

Zhang, Hui, , Jiang, Xiaoyun, , & (2018) A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation. 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)

Liu, Lin, Zheng, Liancun, & (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. (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)

Zheng, Minling, , Liu, Qingxia, , & (2017) Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. 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/)

, Li, Changpin, , & (2015) Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy. 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/)

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, , , & Zhuang, P (2004) Numerical Simulation for Solute Transport in Fractal Porous Media. 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.

, , , & Zhuang, P (2003) Time Fractional Advection-Dispersion Equation. 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/)

Feng, Libo (2019) Numerical investigation and application of fractional dynamical systems. PhD by Publication, Queensland University of Technology. (https://eprints.qut.edu.au/126980/)