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/)

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/)

, Meerschaert, Mark, McGough, Robert, Zhuang, Pinghui, & Liu, Qingxia (2013) Numerical methods for solving the multi-term time-fractional wave-diffusion equation. Fractional Calculus and Applied Analysis, 16(1), pp. 9-25. (https://eprints.qut.edu.au/76841/)

, , , & (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. (https://eprints.qut.edu.au/77141/)

Jiang, H., , 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. (https://eprints.qut.edu.au/113211/)

Chen, Chang-Ming, , , , & Chen, Y. (2013) Numerical approximation for a variable-order nonlinear reaction-subdiffusion equation. Numerical Algorithms, 63(2), pp. 265-290. (https://eprints.qut.edu.au/60016/)

Shen, S., , , , & 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. (https://eprints.qut.edu.au/77100/)

Zhang, H., , 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. (https://eprints.qut.edu.au/76867/)

, , , & (2013) Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D. Open Physics, 11(6), pp. 646-665. (https://eprints.qut.edu.au/111581/)

Ye, H., , , , & (2013) Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions. European Physical Journal: Special Topics, 222(8), pp. 1901-1914. (https://eprints.qut.edu.au/77000/)

, , , , & (2013) A numerical method for the fractional Fitzhugh-Nagumo monodomain model. The ANZIAM Journal, 54, C608-C629. (https://eprints.qut.edu.au/79808/)

Zeng, F., Li, C., & (2013) High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations. European Physical Journal: Special Topics, 222(8), pp. 1885-1900. (https://eprints.qut.edu.au/77108/)

, Li, Changpin, , & (2013) The use of finite difference/element approaches for solving the time-fractional subdiffusion equation. SIAM Journal of Scientific Computing, 35(6), A2976-A3000. (https://eprints.qut.edu.au/77030/)

Chen, Shiping, , , & (2013) An implicit numerical method for the two-dimensional fractional percolation equation. Applied Mathematics and Computation, 219(9), pp. 4322-4331. (https://eprints.qut.edu.au/77313/)

, Cheng, Shiping, , , & (2013) Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term. Open Physics, 11(10), pp. 1221-1232. (https://eprints.qut.edu.au/111582/)

Chen, Chang-Ming, , , & 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. (https://eprints.qut.edu.au/60015/)

Chen, J., , , & 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. (https://eprints.qut.edu.au/59964/)

, , & Hamilton, Nicholas (2013) Some novel techniques of parameter estimation for dynamical models in biological systems. IMA Journal of Applied Mathematics, 78(2), pp. 235-260. (https://eprints.qut.edu.au/45865/)

, , , , & Vegh, V. (2012) The use of a Riesz fractional differential-based approach for texture enhancement in image processing. In The 16th Biennial Computational Techniques and Applications Conference, 2012-09-23 - 2012-09-26. (https://eprints.qut.edu.au/60007/)

, , & (2012) A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. In Sun, H, Chen, W, & Baleanu, D (Eds.) Proceedings of the 5th IFAC Symposium on Fractional Differentiation and Its Applications. Hohai University, China, pp. 1-6. (https://eprints.qut.edu.au/51457/)

, , & (2012) A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients. In 16th Biennial Computational Techniques and Applications Conference, 2012-09-23 - 2012-09-26. (https://eprints.qut.edu.au/60008/)

, Zhuang, Pinghui, & (2012) Numerical methods and analysis for a class of fractional advection-dispersion models. Computers and Mathematics with Applications, 64(10), pp. 2990-3007. (https://eprints.qut.edu.au/51515/)

, , , & (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. (https://eprints.qut.edu.au/51516/)

Shen, Shujun, , Chen, Jing, , & (2012) Numerical techniques for the variable order time fractional diffusion equation. Applied Mathematics and Computation, 218(22), pp. 10861-10870. (https://eprints.qut.edu.au/51509/)

Chen, Chang-Ming, , , & (2012) Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation. Mathematics of Computation, 81(277), pp. 345-366. (https://eprints.qut.edu.au/51510/)

Li, Changpin, , & (2012) Spectral approximations to the fractional integral and derivative. Fractional Calculus and Applied Analysis, 15(3), pp. 383-406. (https://eprints.qut.edu.au/60013/)

Chen, J., , , 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. (https://eprints.qut.edu.au/60021/)

, , , & (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. (https://eprints.qut.edu.au/60023/)

, , , & (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. (https://eprints.qut.edu.au/51507/)

Zhuang, Pinghui, , , , & (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. (https://eprints.qut.edu.au/45619/)

& (2011) Novel techniques in parameter estimation for fractional dynamical models arising from biological systems. Computers and Mathematics with Applications, 62(3), pp. 822-833. (https://eprints.qut.edu.au/52468/)

, , , & (2011) Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions. SIAM Journal of Scientific Computing, 33(3), pp. 1159-1180. (https://eprints.qut.edu.au/40662/)

Liu, Q., , , & (2011) Finite element approximation for a modified anomalous subdiffusion equation. Applied Mathematical Modelling, 35(8), pp. 4103-4116. (https://eprints.qut.edu.au/52255/)

Chen, Chang-Ming, , , & (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. (https://eprints.qut.edu.au/52621/)

Shen, Shujun, , & (2011) Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation. Numerical Algorithms, 56(3), pp. 383-403. (https://eprints.qut.edu.au/42736/)

Chen, Shiping, , & (2011) A novel implicit finite difference method for the one-dimensional fractional percolation equation. Numerical Algorithms, 56(4), pp. 517-535. (https://eprints.qut.edu.au/43080/)

Liu, Q., , Zhuang, Pinghui, , & Nie, Yufeng (2011) An implicit RBF meshless approach for time fractional diffusion equations. Computational Mechanics, 48(1), pp. 1-12. (https://eprints.qut.edu.au/45681/)

, , & (2011) Two new implicit numerical methods for the fractional cable equation. Journal of Computational and Nonlinear Dynamics, 6(1), pp. 1-7. (https://eprints.qut.edu.au/37944/)

Chen, Chang-Ming, , , & (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. (https://eprints.qut.edu.au/42692/)

, , , , & (2011) Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions. In McLean, W & Roberts, T (Eds.) 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/)

Chen, Chang-Ming, , & (2011) Numerical analysis for a variable-order nonlinear cable equation. Journal of Computational and Applied Mathematics, 236(2), pp. 209-224. (https://eprints.qut.edu.au/45864/)

Chen, Chang-Ming, , , & (2010) Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equations. SIAM Journal on Computing, 32(4), pp. 1740-1760. (https://eprints.qut.edu.au/42998/)

, , , & (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. (https://eprints.qut.edu.au/42795/)

Zhang, H., , & (2010) Galerkin finite element approximation of symmetric space-fractional partial differential equations. Applied Mathematics and Computation, 217(6), pp. 2534-2545. (https://eprints.qut.edu.au/43293/)

, , & (2010) Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. 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.)

Chen, Chang-Ming, , , & (2010) Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation. Numerical Algorithms, 54(1), pp. 1-21. (https://eprints.qut.edu.au/29756/)

& (2010) Parameter estimation for fractional dynamical models in biological systems. In Chen, Podlubny, I, Vinagre Jara, B M, Feliu Batlle, V, & Tejado Balsera, I (Eds.) 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/)

Zhuang, Pinghui, , , & (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. (https://eprints.qut.edu.au/29755/)

, Yang, Chen, & (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. (https://eprints.qut.edu.au/29754/)

, , & (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, 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.

Lin, R, , , & (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. (https://eprints.qut.edu.au/29758/)

Zhuang, Pinghui, , , & (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. (https://eprints.qut.edu.au/29759/)

Liu, Q, , , & (2009) Numerical simulation for the 3D seepage flow with fractional derivatives in porous media. IMA Journal of Applied Mathematics, 74(2), pp. 201-229. (https://eprints.qut.edu.au/29757/)

Chen, S, , Zhuang, Pinghui, & (2009) Finite Difference Approximations for the Fractional Fokker-Planck Equation. Applied Mathematical Modelling, 33(1), pp. 256-273. (https://eprints.qut.edu.au/14804/)

Yu, Q, Song, J, , , & (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. (https://eprints.qut.edu.au/42823/)

Chen, Chang-Ming, , & (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. (https://eprints.qut.edu.au/30935/)

Chen, Chang-Ming & (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. (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.

Chen, S & (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. (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.

Shen, Shujun, , & (2008) Fundamental solution and discrete random walk model for time-space fractional diffusion equation of distributed order. Journal of Applied Mathematics and Computing, 28(1-2), pp. 147-164. (https://eprints.qut.edu.au/30922/)

Zhuang, Pinghui, , , & (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. (https://eprints.qut.edu.au/30905/)

Zhang, Hong-Mei & (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. (https://eprints.qut.edu.au/30897/)

Chen, Chang-Ming, , & (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. (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.

Shen, S, , , & (2008) The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation. IMA Journal of Applied Mathematics, 73, pp. 850-872. (https://eprints.qut.edu.au/30652/)

Yu, Q, , , & (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. (https://eprints.qut.edu.au/43102/)

Chen, Jing, , & (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. (https://eprints.qut.edu.au/43041/)

Huang, F & (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. (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 .

Chen, Chang-ming, , & (2008) Finite Difference Methods and a Fourier Analysis for the Fractional Reaction-Subdiffusion Equation. Applied Mathematics and Computation, 198(2), pp. 754-769. (https://eprints.qut.edu.au/14755/)

Chen, Chang-ming, , , & (2007) A Fourier method for the fractional diffusion equation describing sub-diffusion. Journal of Computational Physics, 227(2), pp. 886-897. (https://eprints.qut.edu.au/14739/)

Zhuang, Pinghui & (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. (https://eprints.qut.edu.au/14892/)

Zhang, H, , & (2007) Numerical Approximation of Levy-Feller Diffusion Equation and its Probability Interpretation. Journal of Computational and Applied Mathematics, 206(2), pp. 1098-1115. (https://eprints.qut.edu.au/10482/)

Liu, Q, , , & (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. (https://eprints.qut.edu.au/10478/)

Zhuang, Pinghui & (2007) Finite Difference Approximation for Two-Dimensional Time Fractional Diffusion Equation. Journal of Algorithms and Computational Technology, 1(1), pp. 1-15. (https://eprints.qut.edu.au/15085/)

Cai, Xin & (2007) Numerical Simulation of the Fractional-Order Control System. Journal of Applied Mathematics and Computing, 23(1-2), pp. 229-241. (https://eprints.qut.edu.au/14891/)

Lin, R & (2007) Fractional High Order Methods For The Nonlinear Fractional Ordinary Differential Equation. Nonlinear Analysis: Modelling and Control, 66(4), pp. 856-869. (https://eprints.qut.edu.au/21852/)

, Zhuang, Pinghui, , , & (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. (https://eprints.qut.edu.au/44379/)

Chen, Chang-ming, , , & (2007) Implicit Difference Approximation of the Galilei Invariant Fractional Advection Diffusion Equation. 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.

Chen, Jing & (2007) Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation. 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.

Zhang, Hongmei & (2007) The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions. Numerical Mathematics, 16(2), pp. 181-192. (https://eprints.qut.edu.au/42817/)

Zhuang, Pinghui, , , & (2007) Numerical Treatment For The Fractional Fokker-Planck Equation. 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.

Yin, Cui-ying, , & (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. (https://eprints.qut.edu.au/15090/)

Zhuang, Pinghui & (2006) Implicit Difference Approximation for the Time Fractional Diffusion Equation. Journal of Applied Mathematics and Computing, 22(3), pp. 87-99. (https://eprints.qut.edu.au/23700/)

, , , & (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. (https://eprints.qut.edu.au/23835/)

, Zhuang, P, , & (2006) A Fractional-Order Implicit Difference Approximation For the Space-Time Fractional Diffusion Equation. In Blyth, B, Stacey, A, & Shepherd, J (Eds.) 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/)

Yang, C & (2006) A Computationally Effective Predictor-Corrector Method for Simulating Fractional Order Dynamical Control System. In Blyth, B, Stacey, A, & Shepherd, J (Eds.) 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 .

Shen, Shujun, , , & (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. (https://eprints.qut.edu.au/23024/)

, , , Bajracharya, Kiran, Huxley, W, & (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. (https://eprints.qut.edu.au/10479/)

Huang, Fenghui & (2005) The Fundamental Solution of the Space-Time Fractional Advection-Dispersion Equation. Journal of Applied Mathematics and Computing, 18(1 - 2), pp. 339-350. (https://eprints.qut.edu.au/23460/)

Huang, Fenghui & (2005) The Space-Time Fractional Diffusion Equation with Caputo Derivatives. Journal of Applied Mathematics and Computing, 19(1 - 2), pp. 179-190. (https://eprints.qut.edu.au/21880/)

Huang, F & (2005) The Time Fractional Diffusion Equation and the Advection-Dispersion Equation. The ANZIAM Journal, 46, pp. 317-330. (https://eprints.qut.edu.au/23432/)

Shen, S & (2005) Error Analysis of an Explicit Finite Difference Approximation for the Space Fractional Diffusion Equation with Insulated Ends. In May, R (Ed.) 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.

Su, Ninghu, Sander, G, , , & 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. (https://eprints.qut.edu.au/22531/)

, Shen, S, , & (2004) Analysis of a Discrete non-Markovian Random Walk Approximation for the Time Fractional Diffusion Equation. The ANZIAM Journal, 46(5), C488-C504. (https://eprints.qut.edu.au/22160/)

, , & (2004) Numerical Solution of the Space Fractional Fokker-Planck Equation. Journal of Computational and Applied Mathematics, 166, pp. 209-219. (https://eprints.qut.edu.au/10113/)

, , , & 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/)