[1]
Baeumer B., Kovcs M. and Sankaranarayanan H., Higher order Grünwald approximations of fractional derivatives and fractional powers of operators, Trans. Amer. Math. Soc., 367 (2015), pp. 813–834.

[2]
Benson D. A., Wheatcraft S. W. and Meerschaert M. M., The fractional-order governing equation of Lévy motion, Water Resour. Res., 36 (2000), pp. 1413–1423.

[3]
ÇElik C. and Duman M., Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative, J. Comput. Phys., 231 (2012), pp. 1743–1750.

[4]
Chan T. F., Stability analysis of finite difference schemes for the advection-diffusion equation, SIAM J. Numer. Anal., 21 (1984), pp. 272–284.

[5]
Chen M. H., Deng W. H. and Wu Y. J., Superlinearly convergent algorithms for the two dimensional space-time Caputo-Riesz fractional diffusion equation, Appl. Numer. Math., 70 (2013), pp. 22–41.

[6]
Deng Z. Q., Singh V. P., Asce F. and Bengtsson L., Numerical solution of fractional advection-dispersion different equations, J. Hydral. Eng., 130 (2004), pp. 422–431.

[7]
Dyakonov E. G., Difference schemes of second-order accuracy with a splitting operator for parabolic equations without mixed derivatives, Zh. Vychisl. Mat. I Mat. Fiz., 4 (1964), pp. 935–941.

[8]
Fornberg B., Calculation of weights in finite difference formulas, SIAM Rev., 40 (1998), pp. 685–691.

[9]
Gustafsson B., Kreiss H.-O. and Oliger J., Time Dependent Problems and Difference Methods, Wiley Interscience, New York, 1995.

[10]
Liu F., Ahn V. and Turner I., Numerical solution of the space fractional Fokker-Planck equation, J. Comput. Appl. Math., 166 (2004), pp. 209–219.

[11]
Lubich Ch., Discretized fractional calculus, SIAM J. Math. Anal., 17 (1986), pp. 704–719.

[12]
Lynch V. E., Carreras B. A., Del-Castillo-Negrete D., Ferreira-Mejias K. M. and Hicks H. R., Numerical methods for the solution of partial differential equations of fractional order, J. Comput. Phys., 192 (2003), pp. 406–421.

[13]
Meerschaert M. M. and Tadjeran C., Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math., 172 (2004), pp. 65–77.

[14]
Meerschaert M. M., Scheffler H.-P. and Tadjeran C., Finite difference methods for two-dimensional fractional dispersion equation, J. Comput. Phys., 211 (2006), pp. 249–261.

[15]
Meerschaert M. M. and Tadjeran C., Finite difference approximations for two-sided space-fractional partial differential equations, Appl. Numer. Math., 56 (2006), pp. 80–90.

[16]
Metzler R. and Klafter J., The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A Math. General, 37 (2004), pp. 161–208.

[17]
Metzler R. and Klafter J., The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339 (2000), pp. 1–77.

[18]
Oldham K. B. and Spanier J., The fractional calculus, Academic Press, New York, 1974.

[19]
Ortigueira M. D., Riesz potential operators and inverses via fractional centred derivatives, Int. J. Math. Math. Sci., 2006 (2006), pp. 1–12.

[20]
Pang H.-K. and Sun H. W., Multigrid method for fractional diffusion equations, J. Comput. Phys., 231 (2012), pp. 693–703.

[21]
Peaceman D. W. and Rachford H. H. Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3 (1959), pp. 28–41.

[22]
Podlubny I., Fractional Differential Equations, Academic Press, San Diego, 1999.

[23]
Song J., Yu Q., Liu F. and Turner I., A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation, Numer. Algorithms, 66 (2014), pp. 911–932.

[24]
Sousa E., Finite difference approximations for a fractional advection diffusion problem, J. Comput. Phys., 228 (2009), pp. 4038–4054.

[25]
Sousa E. and Li C., A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative, Appl. Numer. Math., 90 (2015), pp. 22–37.

[26]
Strikwerda J. C., Finite Difference Schemes and Partial Differential Equations, SIAM, 2004.

[27]
Sun Z. Z., Numerical Methods of Partial Differential Equations (in Chinese), Science Press, Beijing, 2005.

[28]
Thomas J. W., Numerical Partial Differential Equations: Finite Difference Methods, Springer New York, 1995.

[29]
Tuan V. K. and Gorenflo R., Extrapolation to the limit for numerical fractional differentiation, Z. Angew. Math. Mech., 75 (1995), pp. 646–648.

[30]
Tian W. Y., Zhou H. and Deng W. H., A class of second order difference approximations for solving space fractional diffusion equations, Math. Comput., 84 (2015), pp. 1703–1727.

[31]
Wang D. L., Xiao A. G. and Yang W., Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative, J. Comput. Phys., 242 (2013), pp. 670–681.

[32]
Wang H., Wang K. and Sircar T., A direct Nlog^{2}N finite difference method for fractional diffusion equations, J. Comput. Phys., 229 (2010), pp. 8095–8104.