[1] Sokolov, I. M., Klafter, J., and Blumen, A. Fractional kinetics. Physics Today, 55, 48-54 (2002)
[2] Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M. Application of a fractional advection- dispersion equation. Water Resources Research, 36, 1403-1412 (2000)
[3] Benson, D. A.,Wheatcraft, S.W., andMeerschaert, M. M. The fractional-order governing equation of Lévy motion. Water Resources Research, 36, 1413-1423 (2000)
[4] Magin, R. L. Fractional Calculus in Bioengineering, Begell House Publishers, Danbury (2006)
[5] Kirchner, J. W., Feng, X., and Neal, C. Fractal stream chemistry and its implications for contam- inant transport in catchments. nature, 403, 524-527 (2000)
[6] Raberto, M., Scalas, E., and Mainardi, F. Waiting-times and returns in high-frequency financial data: an empirical study. Physica A: Statistical Mechanics and Its Applications, 314, 749-755 (2002)
[7] Liu, F., Anh, V., and Turner, I. Numerical solution of the space fractional Fokker-Planck equation. Journal of Computational and Applied Mathematics, 166, 209-219 (2004)
[8] Ervin, V. J. and Roop, J. P. Variational formulation for the stationary fractional advection dis- persion equation. Numerical Methods for Partial Differential Equations, 22, 558-576 (2005)
[9] Ervin, V. J., Heuer, N., and Roop, J. P. Numerical approximation of a time dependent, non-linear, space-fractional diffusion equation. SIAM Journal on Numerical Analysis, 45, 572-591 (2007)
[10] Meerschaert, M. M. and Tadjeran, C. Finite difference approximations for fractional advection- dispersion flow equations. Journal of Computational and Applied Mathematics, 172, 65-77 (2004)
[11] Meerschaert, M. M., Scheffler, H. P., and Tadjeran, C. Finite difference methods for two- dimensional fractional dispersion equation. Journal of Computational Physics, 211, 249-261 (2006)
[12] Li, X. and Xu, C. Existence and uniqueness of the week solution of the space-time fractional diffu- sion equation and a spectral method approximation. Communications in Computational Physics, 8, 1016-1051 (2010)
[13] Lin, Y., Li, X., and Xu, C. Finite dfiference/specrtal approximations for the fractional cable equation. Mathematics of Computation, 80, 1369-1396 (2011)
[14] Chen, C. M., Liu, F., and Burrage, K. Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. Applied Mathematics and Computation, 198, 754-769 (2008)
[15] Liu, F., Zhuang, P., and Burrage, K. Numerical methods and analysis for a class of fractional advection-dispersion models. Computers and Mathematics with Applications, 64, 2990-3007 (2012)
[16] Shen, S., Liu, F., Anh, V., Turner, I., and Chen, J. A characteristic difference method for the variable-order fractional advection-diffusion equation. Journal of Applied Mathematics and Com- puting, 42, 371-386 (2013)
[17] Liu, F., Meerschaert, M. M., McGough, R. J., Zhuang, P., and Liu, Q. Numerical methods for solving the multi-term time-fractional wave-diffusion equation. Fractional Calculus and Applied Analysis, 16, 9-25 (2013)
[18] Hao, Z. P., Sun, Z. Z., and Cao, W. R. A fourth-order approximation of fractional derivatives with its applications. Journal of Computational Physics, 281, 787-805 (2015)
[19] Zheng, M., Liu, F., Turner, I., and Anh, V. A novel high order space-time spectral method for the time fractional Fokker-Planck equation. SIAM Journal on Scientific Computing, 37, A701-A724 (2015)
[20] Shen, S., Liu, F., Liu, Q., and Anh, V. Numerical simulation of anomalous infiltration in porous media. Numerical Algorithms, 68, 443-454 (2015)
[21] Liu, F., Zhuang, P., Turner, I., Burrage, K., and Anh, V. A new fractional finite volume method for solving the fractional diffusion equation. Applied Mathematical Modelling, 38, 3871-3878 (2014)
[22] Feng, L. B., Zhuang, P., Liu, F., and Turner, I. Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation. Applied Mathematics and Computation, 257, 52-65 (2015)
[23] Liu, Q., Liu, F., Turner, I., Anh, V., and Gu, Y. A RBF meshless approach for modeling a fractal mobile/immobile transport model. Applied Mathematics and Computation, 226, 336-347 (2014)
[24] Liu, Q., Liu, F., Gu, Y., Zhuang, P., Chen, J., and Turner, I. A meshless method based on point interpolation method (PIM) for the space fractional diffusion equation. Applied Mathematics and Computation, 256, 930-938 (2015)
[25] Feng, L., Zhuang, P., Liu, F., Turner, I., and Yang, Q. Second-order approximation for the space fractional diffusion equation with variable coefficient. Progress in Fractional Differentiation and Applications, 1, 23-35 (2015)
[26] Liu, F., Chen, S., Turner, I., Burrage, K., and Anh, V. Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a non-linear reaction term. Central European Jour- nal of Physics, 11, 1221-1232 (2013)
[27] Yang, Q., Turner, I., Moroney, T., and Liu, F. A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations. Applied Mathematical Modelling, 38, 3755-3762 (2014)
[28] Petford, N. and Koenders, M. A. Seepage flow and consolidation in a deforming porous medium. Geophysical Research Abstracts, 5, 13329 (2003)
[29] Thusyanthan, N. I. and Madabhushi, S. P. G. Scaling of Seepage Flow Velocity in Centrifuge Mod- els, Technical Report CUED/D-SOILS/TR326, Engineering Department, Cambridge University, Cambridge, 1-13 (2003)
[30] Chou, H., Lee, B., and Chen, C. The transient infiltration process for seepage flow from cracks. Western Pacific Meeting, Advances in Subsurface Flow and Transport: Eastern and Western Ap- proaches III, American Geophysical Union Meetings Department, Beijing (2006)
[31] Bear, J. Dynamics of Fluids in Porous Media, Elsevier, New York, 184-186 (1972)
[32] He, J. H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering, 167, 57-68 (1998)
[33] Miller, K. S. and Ross, B. An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York (1993)
[34] Samko, S. G., Kilbas, A. A., and Marichev, O. I. Fractional Integrals and Derivatives: Theory and Applications, Gordon Breach, Yverdon (1993)
[35] Podlubny, I. Fractional Differential Equations, Academic Press, New York (1999)
[36] Ochoa-Tapia, J. A., Valdes-Parada, F. J., and Alvarez-Ramirez, J. A fractional-order Darcy's law. Physica A: Statistical Mechanics and Its Applications, 374, 1-14 (2007)
[37] Chen, S., Liu, F., and Anh, V. A novel implicit finite difference methods for the one dimensional fractional percolation equation. Numerical Algorithms, 56, 517-535 (2011)
[38] Chen, S., Liu, F., Turner, I., and Anh, V. An implicit numerical method for the two-dimensional fractional percolation equation. Applied Mathematics and Computation, 219, 4322-4331 (2013)
[39] Chen, S., Liu, F., and Burrage, K. Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Computers and Mathematics with Applications, 68, 2133-2141 (2014)
[40] Liu, Q., Liu, F., Turner, I., and Anh, V. Numerical simulation for the 3D seepage flow with fractional derivatives in porous media. IMA Journal of Applied Mathematics, 74, 201-229 (2009)
[41] Jia, J. and Wang, H. Fast finite difference methods for space-fractional diffusion equations with fractional derivative boundary conditions. Journal of Computational Physics, 293, 359-369 (2015)
[42] Gray, R. M. Toeplitz and circulant matrices: a review. Communications and Information Theory, 2, 155-239 (2006)
[43] Isaacson, E. and Keller, H. B. Analysis of Numerical Methods, Wiley, New York (1966)