1. Alikhanov, A.A.:A new diference scheme for the time fractional difusion equation. J. Comput. Phys. 280, 424-438 (2015)
2. Angstmann, C.N., Henry, B.I., Jacobs, B.A., McGann, A.V.:A time-fractional generalised advection equation from a stochastic process. Chaos Solitons Fractals 102, 175-183 (2017)
3. Benson, D.A., Wheatcraft, S.W., Meerschaert, M.M.:Application of a fractional advection-dispersion equation. Water Resour. Res. 36(6), 1403-1412 (2000)
4. Bouchaud, J.P., Georges, A.:Anomalous difusion in disordered media:statistical mechanisms, models and physical applications. Phys. Rep. 195(4), 127-293 (1990)
5. Celik, C., Duman, M.:Crank-Nicolson method for the fractional difusion equation with the Riesz fractional derivative. J. Comput. Phys. 231(4), 1743-1750 (2012)
6. Chen, C.M., Liu, F., Turner, I., Anh, V.:A Fourier method for the fractional difusion equation describing sub-difusion. J. Comput. Phys. 227(2), 886-897 (2007)
7. Diethelm, K., Ford, J.M., Ford, N.J., Weilbeer, M.:Pitfalls in fast numerical solvers for fractional differential equations. J. Comput. Appl. Math. 186, 482-503 (2006)
8. Ding, H.F., Li, C.P., Chen, Y.Q.:High-order algorithms for Riesz derivative and their applications (I). Abstr. Appl. Anal. 2014, 653797 (2014)
9. Ding, H.F., Li, C.P., Chen, Y.Q.:High-order algorithms for Riesz derivative and their applications (Ⅱ). J. Comput. Phys. 293, 218-237 (2015)
10. Ding, H.F., Li, C.P.:High-order algorithms for Riesz derivative and their applications (Ⅲ). Fract. Calc. Appl. Anal. 19, 19-55 (2016)
11. Ding, H.F., Li, C.P.:High-order numerical algorithms for Riesz derivatives via constructing new generating functions. J. Sci. Comput. 71, 759-784 (2017)
12. Fedotov, S., Iomin, A.:Migration and proliferation dichotomy in tumor-cell invasion. Phys. Rev. Lett. 98(11), 118101 (2007)
13. Henry, B.I., Langlands, T.A.M., Wearne, S.L.:Fractional cable models for spiny neuronal dendrites. Phys. Rev. Lett. 100(12), 128103 (2007)
14. Jiang, H., Liu, F., Turner, I., Burrage, K.:Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-difusion equations on a fnite domain. J. Math. Anal. Appl. 389(2), 1117-1127 (2012)
15. Langlands, T.A.M., Henry, B.I.:The accuracy and stability of an implicit solution method for the fractional difusion equation. J. Comput. Phys. 205(2), 719-736 (2005)
16. Li, C.P., Zeng, F.H.:Numerical Methods for Fractional Calculus. Chapman and Hall/CRC Press, Boca Raton, USA (2015)
17. Li, C.P., Ding, H.F.:Higher order fnite diference method for the reaction and anomalous-difusion equation. Appl. Math. Model. 38(15/16), 3802-3821 (2014)
18. Li, C.P., Yi, Q., Kurths, J.:Fractional convection. J. Comput. Nonlinear Dynam. 13(1), 011004 (2018)
19. Li, J., Liu, F., Feng, L., Turner, I.:A novel fnite volume method for the Riesz space distributed-order advection-difusion equation. Appl. Math. Model. 46, 536-553 (2017)
20. Lubich, C.:Discretized fractional calculus. SIAM J. Math. Anal. 17(3), 704-719 (1986)
21. Metzler, R., Klafter, J.:The random walks guide to anomalous difusion:a fractional dynamics approach. Phys. Rep. 339(1), 1-77 (2000)
22. Oldham, K.B., Spanier, J.:The Fractional Calculus. Academic Press, New York (1974). (renewed 2002)
23. Ortigueira, M.D.:Riesz potential operators and inverses via fractional centred derivatives. Int. J. Math. Math. Sci. 2006, 48391 (2006)
24. Perdikaris, P., Karniadakis, G.E.:Fractional-order viscoelasticity in one-dimensional blood fow models. Ann. Biomed. Eng. 42(5), 1012-1023 (2014)
25. Podlubny, I.:Fractional Diferential Equations. Academic Press, San Diego (1999)
26. Schumer, R., Benson, D.A., Meerschaert, M.M., Wheatcraft, S.W.:Eulerian derivation of the fractional advection-dispersion equation. J. Contam. Hydrol. 48(1), 69-88 (2001)
27. Shen, S., Liu, F., Anh, V.:Fundamental solution and discrete random walk model for a time-space fractional difusion equation of distributed order. J. Appl. Math. Comput. 28(1/2), 147-164 (2008)
28. Shen, S., Liu, F., Anh, V.:Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-difusion equation. Numer. Algorithms 56(3), 383-403 (2011)
29. Shen, S., Liu, F., Anh, V., Turner, I., Chen, J.:A novel numerical approximation for the space fractional advection-dispersion equation. IMA J. Appl. Math. 79(3), 431-444 (2014)
30. Sousa, E.:How to approximate the fractional derivative of order 1 < α ≤ 2. Int. J. Bifurc. Chaos 22(4), 1250075 (2012)
31. Yang, Q., Liu, F., Turner, I.:Numerical methods for fractional partial diferential equations with Riesz space fractional derivatives. Appl. Math. Model. 34(1), 200-218 (2010)
32. Zaslavsky, G.M.:Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, New York (2005)
33. Zeng, F.H., Zhang, Z.Q., Karniadakis, G.E.:Second-order numerical methods for multi-term fractional diferential equations:smooth and non-smooth solutions. Comput. Methods Appl. Mech. Eng. 327, 478-502 (2017)
34. Zhang, H., Liu, F., Jiang, X., Zeng, F., Turner, I.:A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-difusion equation. Comput. Math. Appl. 76, 2460-2476 (2018)
