Project dates: 01/01/2000 - Ongoing
In recent years, fractional models have attracted considerable interest because of their ability to model many phenomena. Anomalous diffusion phenomena are widely spread in nature and engineering, such as diffusion of contaminants, nuclear waste with molecular diffusion, turbulence, controlled drug delivery systems, pollutant flows through porous media, contamination of underground aquifers, propagation of electrical signals in the white matter of the brain, image enhancement, analyzing a particle’s motion in crowded environments, fractional Black-Scholes equations and application and so on.
This project aims to carry out innovative and novel research on developing efficient, robust and accurate computational models for complex fractional dynamical systems. This project involves fractional dynamical systems; numerical methods: finite difference methods; finite element methods; finite control volume methods; meshless methods, and spectral methods; irregular domains; parameter estimation; experimental data and applications.
Chief Investigators
Team
- Dr Libo Feng
- Professor Yang Liu
- Dr Wenping Fan
- Associate Professor Shanzhen Chen
- Professor Yanmin Zhao
- Dr Zeting Liu
- Associate Professor Farah Aini Abdullah
- Associate Professor Yanhua Shi
- Dr Linlin Zhao
- Dr Minling Zheng
- Professor Pinghui Zhuang
- Dr Fanhai Zeng
- Associate Professor Qinxia Liu
- Dr Qianqian Yang
- Professor Hui Jiang
- Professor Shiping Chen
- Dr Qiang Yu
- Associate Professor Hongmei Zhang
Publications
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Shi, Z., Zhao, Y., Liu, Fawang, Wang, F., Tang, Yifa (2018) Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes. Applied Mathematics and Computation, 338, pp.290-304.
- Chen, S., Liu, Fawang, Turner, Ian, Anh, Vo (2018) A fast numerical method for two-dimensional Riesz space fractional diffusion equations on a convex bounded region. Applied Numerical Mathematics, 134, pp.66-80.
- F.A. Abdullah, F. Liu, P. Burrage, K. Burrage, T. Li (2018) Analytical and Numerical Solutions for Fractional Temporal SEIR Measles Model. Numerical Algorithms
- Zheng, Minling, Liu, Fawang, Liu, Qingxia, Burrage, Kevin, Simpson, Matthew (2017) Numerical solution of the time fractional reaction–diffusion equation with a moving boundary. Journal of Computational Physics, 338, pp.493-510.
- 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
- L. Zhao, F. Liu, V. Anh (2017) Numerical methods for the two-dimensional multi-term time-fractional diffusion equations. Computers and Mathematics with Applications
- 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
- X. Zhu, Z. Yuan, F. Liu, Y. Nie (2018) Differential quadrature method for space-fractional diffusion equations on 2D irregular domains. Numerical Algorithms
- 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
- 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
- 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
- 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
- P. Zhuang, F. Liu*, I. Turner and V. Anh (2016) Galerkin finite element method and error analysis for the fractional cable equation. Numerical Algorithms
- 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
- 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
- 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
- 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
- L. Feng, P. Zhuang, F. Liu*, I. Turner and Y. Gu (2015) Finite element method for space-time fractional diffusion equation. Numerical Algorithms
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Liu, Fawang, Meerschaert, Mark, McGough, Robert, Zhuang, Pinghui, Liu, Qingxia (2013) Numerical methods for solving the -term time-fractional wave-diffusion equation. Fractional Calculus and Applied Analysis, 16 (1), pp.9-25.
- Jiang, H., Liu, Fawang, Meerschaert, Mark, McGough, Robert, Liu, Q. (2013) The fundamental solutions for multi-term modified power law wave equations in a finite domain. Electronic Journal of Mathematical Analysis and Applications (EJMAA), 1 (1), pp.55-66.
- Zeng, Fanhai, Li, Changpin, Liu, Fawang, Turner, Ian (2013) The use of finite difference/element approaches for solving the time-fractional subdiffusion equation. SIAM Journal of Scientific Computing, 35 (6), pp.A2976-A3000.
- Zeng, F., Li, C., Liu, Fawang (2013) High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations. European Physical Journal: Special Topics, 222 (8), pp.1885-1900.
- Hejazi, Hala, Moroney, Timothy, Liu, Fawang (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, pp.1-6.
- Chen, Shiping, Liu, Fawang, Turner, Ian, Anh, Vo (2013) An implicit numerical method for the two-dimensional fractional percolation equation. Applied Mathematics and Computation, 219 (9), pp.4322-4331.
- Hejazi, H., Moroney, T., Liu, F. (2012) A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients. 16th Biennial Computational Techniques and Applications Conference.
- Liu, Fawang, Cheng, Shiping, Turner, Ian, Burrage, Kevin, Anh, Vo (2013) Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term. Open Physics, 11 (10), pp.1221-1232.
- Chen, J., Liu, Fawang, Burrage, Kevin, Shen, S. (2013) Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Journal of Applied Mathematics and Computing, 41 (1 - 2), pp.33-47.
- Jiang, Hui, Liu, Fawang, Turner, Ian, Burrage, Kevin (2012) Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. Computers and Mathematics with Applications, 64 (10), pp.3377-3388.
- Li, Changpin, Zeng, Fanhai, Liu, Fawang (2012) Spectral approximations to the fractional integral and derivative. Fractional Calculus and Applied Analysis, 15 (3), pp.383-406.
- Zhuang, Pinghui, Gu, YuanTong, Liu, Fawang, Turner, Ian, Yarlagadda, Prasad (2011) Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method. International Journal for Numerical Methods in Engineering, 88 (13), pp.1346-1362.
- Jiang, Hui, Liu, Fawang, Turner, Ian, Burrage, Kevin (2012) Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. Journal of Mathematical Analysis and Applications, 389 (2), pp.1117-1127.
- Yang, Qianqian, Turner, Ian, Liu, Fawang, Ilic, Milos (2011) Novel numerical methods for solving the time-space fractional diffusion equation in 2D. SIAM Journal of Scientific Computing, 33 (3), pp.1159-1180.
- Chen, Shiping, Liu, Fawang, Anh, Vo (2011) A novel implicit finite difference method for the one-dimensional fractional percolation equation. Numerical Algorithms, 56 (4), pp.517-535.
- Liu, Q., Gu, YuanTong, Zhuang, Pinghui, Liu, Fawang, Nie, Yufeng (2011) An implicit RBF meshless approach for time fractional diffusion equations. Computational Mechanics, 48 (1), pp.1-12.
- Liu, Fawang, Yang, Qianqian, Turner, Ian (2011) Two new implicit numerical methods for the fractional cable equation. Journal of Computational and Nonlinear Dynamics, 6 (1), pp.1-7.
- Yang, Qianqian, Moroney, Timothy, Burrage, Kevin, Turner, Ian, Liu, Fawang (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, pp.C395-C409.
- Zhang, H., Liu, Fawang, Anh, Vo (2010) Galerkin finite element approximation of symmetric space-fractional partial differential equations. Applied Mathematics and Computation, 217 (6), pp.2534-2545.
- Yang, Qianqian, Liu, Fawang, Turner, Ian (2010) Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. Applied Mathematical Modelling, 34 (1), pp.200-218.
- 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
- Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo (2010) Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation. Numerical Algorithms, 54 (1), pp.1-21.
- Liu, Fawang, Yang, Chen, Burrage, Kevin (2009) Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. Journal of Computational and Applied Mathematics, 231 (1), pp.160-176.
- Yang, Qianqian, Turner, Ian, Liu, Fawang (2009) Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation. Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM), 50, pp.C800-C814.
- Q. Yang, F. Liu*, I. Turner (2009) Computationally efficient numerical methods for time and space fractional Fokker-Planck equations. Physica Scripta
- Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process. IMA Journal of Applied Mathematics, 74 (5), pp.645-667.
- Liu, Q, Liu, Fawang, Turner, Ian, Anh, Vo (2009) Numerical simulation for the 3D seepage flow with fractional derivatives in porous media. IMA Journal of Applied Mathematics, 74 (2), pp.201-229.
- Chen, S, Liu, Fawang, Zhuang, Pinghui, Anh, Vo (2009) Finite difference approximations for the fractional Fokker–Planck equation. Applied Mathematical Modelling, 33 (1), pp.256-273.
- Yu, Q, Song, J, Liu, Fawang, Anh, Vo, Turner, Ian (2009) An approximate solution for the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model using the Adomian decomposition method. Journal of Algorithms and Computational Technology, 3 (4), pp.553-571.
- Chen, Chang-Ming, Liu, Fawang, Anh, Vo (2009) A Fourier method and an extrapolation technique for Stokes' first problem for a heated generalized second grade fluid with fractional derivative. Journal of Computational and Applied Mathematics, 223 (2), pp.777-789.
- Chen, Chang-Ming, Liu, Fawang (2009) A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation. Journal of Applied Mathematics and Computing, 30 (1-2), pp.219-236.
- Chen, S, Liu, Fawang (2008) ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation. Journal of Applied Mathematics and Computing, 26 (1-2), pp.295-311.
- Y. Lin and F. Liu (2008) Analytical Solution for the nonhomogeneous anomalous subdiffusion equation. Journal of Xiamen University
- Shen, Shujun, Liu, Fawang, Anh, Vo (2008) Fundamental solution and discrete random walk model for time-space fractional diffusion equation. Journal of Applied Mathematics and Computing, 28 (1-2), pp.147-164.
- Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2008) New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. SIAM Journal on Numerical Analysis, 46 (2), pp.1079-1095.
- Zhang, Hong-Mei, Liu, Fawang (2008) Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term. Journal of Applied Mathematics and Computing, 26 (1-2), pp.1-14.
- Chen, Chang-Ming, Liu, Fawang, Anh, Vo (2008) Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives. Applied Mathematics and Computation, 204, pp.340-351.
- S. Shen and F. Liu (2008) A Computationally Efficient Solution Method for a Riesz Space Fractional Advection-Dispersion Equation. Journal of Xiamen University
- Shen, S, Liu, Fawang, Anh, Vo, Turner, Ian (2008) The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation. IMA Journal of Applied Mathematics, 73, pp.850-872.
- Yu, Q, Liu, Fawang, Anh, Vo, Turner, Ian (2008) Solving linear and non-linear space-time fractional reaction-diffusion equations by the adomian decomposition method. International Journal for Numerical Methods in Engineering, 74 (1), pp.138-158.
- Chen, Jing, Liu, Fawang, Anh, Vo (2008) Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables. Journal of Mathematical Analysis and Applications, 338 (2), pp.1364-1377.
- J. Chen, F. Liu*, I. Turner and V. Anh (2008) The fundamental and numerical solutions of the Riesz space fractional reaction-dispersion equation. ANZIAM J.
- H. Zhang and F. Liu (2008) The solution of a special form of the time fractional Navier-Stokes equations. Chinese Journal of Engineering Mathematics
- 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
- Chen, Chang-ming, Liu, Fawang, Burrage, Kevin (2008) Finite difference methods and a fourier analysis for the fractional reaction–subdiffusion equation. Applied Mathematics and Computation, 198 (2), pp.754-769.
- Zhuang, Pinghui, Liu, Fawang (2007) Implicit difference approximation for the two-dimensional space-time fractional diffusion equation. Journal of Applied Mathematics and Computing, 25 (1-2), pp.269-282.
- Zhang, H, Liu, Fawang, Anh, Vo (2007) Numerical approximation of Levy–Feller diffusion equation and its probability interpretation. Journal of Computational and Applied Mathematics, 206 (2), pp.1098-1115.
- Liu, Q, Liu, Fawang, Turner, Ian, Anh, Vo (2007) Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method. Journal of Computational Physics, 222 (1), pp.57-70.
- Zhuang, Pinghui, Liu, Fawang (2007) Finite difference approximation for two-dimensional time fractional diffusion equation. Journal of Algorithms and Computational Technology, 1 (1), pp.1-15.
- Cai, Xin, Liu, Fawang (2007) Numerical simulation of the fractional-order control system. Journal of Applied Mathematics and Computing, 23 (1-2), pp.229-241.
- Lin, R, Liu, Fawang (2007) Fractional High Order Methods For The Nonlinear Fractional Ordinary Differential Equation. Nonlinear Analysis: Modelling and Control, 66 (4), pp.856-869.
- Liu, Fawang, Zhuang, Pinghui, Anh, Vo, Turner, Ian, Burrage, Kevin (2007) Stability and convergence next term of the difference methods for the space-time fractional advection-diffusion equation. Applied Mathematics and Computation, 191 (1), pp.12-20.
- Chen, Chang-ming, Liu, Fawang, Turner, Ian, Anh, Vo (2007) Implicit Difference Approximation of the Galilei Invariant Fractional Advection Diffusion Equation. The ANZIAM Journal, 48 (Supp), pp.Article number: CTAC 775-789.
- H. Zhang and F. Liu (2007) A solution technique of the time-fractional telegraph equation. Journal of Xiamen University
- C. Yin and F. Liu (2007) Some techniques for solving the fractional differential Equations of Endolymph. Journal of Xiamen University
- X. Zhang and F. Liu (2007) Analytical solution of one dimensional fractional diffusion-wave equation under mixed boundary conditions. Journal of Fuzhou University
- X. Wang and F. Liu (2007) Separation of Variables Method for fractional diffusion-wave equation with initial-boundary value problem in three dimension. Journal of Fuzhou University
- H. Zhang and F. Liu (2007) Super linear convergence approximation of the space fractional diffusion equation. Journal of Xiamen University
- Chen, Jing, Liu, Fawang (2007) Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation. Numerical Mathematics, 16 (3), pp.253-264.
- X. Cai and F. Liu (2007) A high order implicit method for the Riesz space fractional diffusion equation. Journal of Xiamen University
- J. Song, F. Liu and P. ,Zhuang (2007) An approximate solution for the non-linear anomalous subdiffusion equation using the Adomian decomposition method. Journal of Xiamen University
- Zhang, Hongmei, Liu, Fawang (2007) The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions. Numerical Mathematics, 16 (2), pp.181-192.
- Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2007) Numerical Treatment For The Fractional Fokker-Planck Equation. The ANZIAM Journal, 48 (Supp), pp.Article number: CTAC 759-774.
- Y. Lin, P. Zhuang and F. Liu (2007) Fractional high order approximation for the system of the nonlinear fractional ordinary differential equations. Journal of Xiamen University
- Yin, Cui-ying, Liu, Fawang, Anh, Vo (2007) Numerical simulation of the nonlinear fractional dynamical systems with fractional damping for the extensible and inextensible pendulum. Journal of Algorithms and Computational Technology, 1 (4), pp.427-447.
- Zhuang, Pinghui, Liu, Fawang (2006) Implicit difference approximation for the time fractional diffusion equation. Journal of Applied Mathematics and Computing, 22 (3), pp.87-99.
- Ilic, Milos, Liu, Fawang, Turner, Ian, Anh, Vo (2006) Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions. Fractional Calculus and Applied Analysis, 9 (4), pp.333-349.
- Liu, Fawang, Zhuang, P, Anh, Vo, Turner, Ian (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), pp.48-68.
- Yang, C, Liu, Fawang (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), pp.168-184.
- Q. Liu and F. Liu (2006) Lévy -Feller advection-diffusion equation. Journal of Xiamen University
- Q. Yu and F. Liu (2006) Implicit difference approximation for the time-fractional order reaction-diffusion equation. Journal of Xiamen University
- Shen, Shujun, Liu, Fawang, Anh, Vo, Turner, Ian (2006) Detailed analysis of a conservative difference approximation for the time fractional diffusion equation. Journal of Applied Mathematics and Computing, 22 (3), pp.1-19.
- Liu, Fawang, Shen, S, Anh, Vo, Turner, Ian (2004) Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation. The ANZIAM Journal, 46 (5), pp.C488-C504.
- Huang, Fenghui, Liu, Fawang (2005) The Fundamental Solution of the Space-Time Fractional Advection-Dispersion Equation. Journal of Applied Mathematics and Computing, 18 (1 - 2), pp.339-350.
- Huang, Fenghui, Liu, Fawang (2005) The Space-Time Fractional Diffusion Equation with Caputo Derivatives. Journal of Applied Mathematics and Computing, 19 (1 - 2), pp.179-190.
- Huang, F, Liu, Fawang (2005) The Time Fractional Diffusion Equation and the Advection-Dispersion Equation. The ANZIAM Journal, 46, pp.317-330.
- Shen, S, Liu, Fawang (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, pp.872-887.
- M. Ilic, F. Liu*, I. Turner and V. Anh (2005) Numerical approximation of a fractional-in-space diffusion equation (I). Fractional Calculus and Applied Analysis
- X. Lu and F. Liu (2005) Time Fractional Diffusion-Reaction Equation. Numerical Mathematics: A Journal of Chinese Universities
- C. Yang and F. Liu (2005) A fractional Predictor-Corrector method of the fractional Relaxation-Oscillation equation. Journal of Xiamen University
- P. Zhuang and F. Liu (2005) An explicit difference approximation for the space-time fractional diffusion equation. Numerical Mathematics: A Journal of Chinese Universities
- Su, Ninghu, Sander, G, Liu, Fawang, Anh, Vo, Barry, D (2005) Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity. Applied Mathematical Modelling, 29 (9), pp.852-870.
- Liu, Fawang, Anh, Vo, Turner, Ian (2004) Numerical solution of the space fractional Fokker-Planck equation. Journal of Computational and Applied Mathematics, 166, pp.209-219.
- R. Lin and F. Liu (2004) A high order approximation of fractional order ordinary differential equation initial value problem. Journal of Xiamen University
- S. Shen and F. Liu (2004) A computational effective method for fractional order Bagley-Torvik equation. Journal of Xiamen University
- X. Lu and F. Liu (2004) The explicit and implicit finite difference approximations for a space fractional advection diffusion equation. Computational Mechanics
- S. Shen and F. Liu (2004) A fully discrete difference approximation for the time fractional diffusion equation. Computational Mechanics
- Liu, Fawang, Anh, Vo, Turner, Ian, Zhuang, P (2003) Time fractional advection-dispersion equation. Journal of Applied Mathematics and Computing, 13 (1-2), pp.233-245.
