1. Aceto, L., Novati, P.:Rational approximation to the fractional Laplacian operator in reaction-difusion problems. SIAM J. Sci. Comput. 39(1), A214-A228 (2017)
2. Baleanu, D., Golmankhaneh, A.K., Nigmatullin, R., Golmankhaneh, A.K.:Fractional Newtonian mechanics. Cent. Eur. J. Phys. 8, 120-125 (2010)
3. Bueno-Orovio, A., Kay, D., Burrage, K.:Fourier spectral methods for fractional-in-space reaction-diffusion equations. BIT Numer. Math. 54, 937-954 (2014)
4. Burrage, K., Hale, N., Kay, D.:An efcient implicit FEM scheme for fractional-in-space reaction-diffusion equations. SIAM J. Sci. Comput. 34(4), A2145-A2172 (2012)
5. Cabré, X., Sire, Y.:Nonlinear equations for fractional Laplacians Ⅱ:existence, uniqueness, and qualitative properties of solutions. Trans. Am. Math. Soc. 367(2), 911-941 (2015)
6. Cabré, X., Tan, J.:Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224(5), 2052-2093 (2010)
7. 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)
8. Chen, S., Jiang, X., Liu, F., Turner, I.:High order unconditionally stable diference schemes for the Riesz space-fractional telegraph equation. J. Comput. Appl. Math. 278, 119-129 (2015)
9. Dehghan, M., Abbaszadeh, M., Mohebbi, A.:Analysis of two methods based on Galerkin weak form for fractional difusion-wave:meshless interpolating element free Galerkin (IEFG) and fnite element methods. Eng. Anal. Bound. Elem. 64, 205-221 (2016)
10. Dehghan, M., Safarpoor, M.:The dual reciprocity boundary elements method for the linear and nonlinear two-dimensional time-fractional partial diferential equations. Math. Methods Appl. Sci. 39, 3979-3995 (2016)
11. Ervin, V.J., Heuer, N., Roop, J.P.:Numerical approximation of a time dependent, nonlinear, spacefractional difusion equation. SIAM J. Numer. Anal. 45, 572-591 (2007)
12. Fei Ding, H., Xin Zhang, Y.:New numerical methods for the Riesz space fractional partial diferential equations. Comput. Math. Appl. 63(7), 1135-1146 (2012)
13. Frank, R.L., Lenzmann, E.:Uniqueness of non-linear ground states for fractional Laplacians in R. Acta Math. 210(2), 261-318 (2013)
14. Hilfer, R.:Applications of Fractional Calculus in Physics. World Scientifc, Singapore (2000)
15. Ilić, M., Liu, F., Turner, I., Anh, V.:Numerical approximation of a fractional-in-space difusion equation I. Fract. Calc. Appl. Anal. 8, 323-341 (2005)
16. Ilić, M., Liu, F., Turner, I., Anh, V.:Numerical approximation of a fractional-in-space difusion equation (Ⅱ) with nonhomogeneous boundary conditions. Fract. Calc. Appl. Anal. 9, 333-349 (2006)
17. Khaliq, A.Q.M., Biala, T.A., Alzahrani, S.S., Faruti, K.M.:Linearly implicit predictor-corrector methods for space-fractional reaction-difusion equations with non-smooth initial data. Comp. Math. Appl. 75, 2629-2657 (2018)
18. Khaliq, A.Q.M., Liang, X., Furati, K.M.:A fourth-order implicit-explicit scheme for the spacefractional nonlinear Schrödinger equations. Numer. Algorithms 75, 147-172 (2017)
19. Lambart, J.D.:Numerical Methods for Ordinary Diferential Systems:The Initial Value Problem. Wiley, New York (1991)
20. Laskin, N.:Fractional Schrödinger equation. Phys. Rev. E 66, 056108 (2002)
21. Lawson, J.D., Morris, J.L.:The extrapolation of frst order methods for parabolic partial diferential equations. SIAM J. Numer. Anal. 15(6), 1212-1224 (1978)
22. Li, D.F., Zhang, C.J., Wang, W.S., Zhang, Y.J.:Implicit-explicit predictor-corrector schemes for nonlinear parabolic diferential equations. Appl. Math. Model. 35, 2711-2722 (2011)
23. Liu, F., Anh, V., Turner, I.:Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 166(1), 209-219 (2004)
24. Liu, F., Yang, C., Burrage, K.:Numerical method and analytical technique of the modifed anomalous subdifusion equation with a nonlinear source term. J. Comput. Appl. Math. 231, 160-176 (2009)
25. Meerschaert, M.M., Tadjeran, C.:Finite diference approximations for fractional advection dispersion fow equations. J. Comput. Appl. Math. 172(1), 65-77 (2004)
26. Meerschaert, M.M., Tadjeran, C.:Finite diference approximations for two-sided space-fractional partial diferential equations. Appl. Numer. Math. 56(1), 80-90 (2006)
27. Metzler, R., Klafter, J.:The random walk's guide to anomalous difusion:a fractional dynamics approach. Phys. Rep. 339, 1-77 (2000)
28. Metzler, R., Klafter, J.:The restaurant at the end of the random walk:recent developments in the description of anomalous transport by fractional dynamics. J. Phys. Math. Gen. 37, R161-R208 (2004)
29. Momani, S., Qaralleh, R.:Numerical approximations and Padé approximants for a fractional population growth model. Appl. Math. Model. 31, 1907-1914 (2007)
30. Ochoa-Tapia, J.A., Valdes-Parada, F.J., Alvarez-Ramirez, J.:A fractional-order Darcy's law. Phys. A Stat. Mech. Appl. 374, 1-14 (2007)
31. Podlubny, I.:Fractional Diferential Equations in Mathematics, Science and Engineering, vol. 198. Academic Press, New York (1999)
32. Saadatmandi, A., Dehghan, M., Azizi, M.:The Sinc-Legendre collocation method for a class of fractional convection-difusion equation with variable coefcients. Commun. Nonlinear Sci. Numer. Simul. 17(11), 4125-4136 (2012)
33. Samko, S.G., Kilbas, A.A., Marichev, O.I.:Fractional Integrals and Derivatives:Theory and Applications. Gordon and Breach Science Publishers, New York (1987)
34. Smith, G.D.:Numerical Solution of Partial Diferential Equations:Finite Diference Methods. Clarendon Press, Oxford (1985)
35. Sousa, E.:Finite diference approximations for a fractional advection difusion problem. J. Comput. Phys. 228(11), 4038-4054 (2009)
36. Sousa, E., Li, C.:A weighted fnite diference method for the fractional difusion equation based on the Riemann-Liouville derivative. Appl. Numer. Math. 90, 22-37 (2015)
37. Tadjeran, C., Meerschaert, M.M., Schefer, H.P.:A second-order accurate numerical approximation for the fractional difusion equation. J. Comput. Phys. 213(1), 205-213 (2006)
38. Valdes-Parada, F.J., Ochoa-Tapia, J.A., Alvarez-Ramirez, J.:Efective medium equations for fractional Fick's law in porous media. Phys. A Stat. Mech. Appl. 373, 339-353 (2007)
39. Voss, D.A., Casper, M.J.:Efcient split linear multistep methods for stif ODEs. SIAM J. Sci. Stat. Comput. 10, 990-999 (1989)
40. Voss, D.A., Khaliq, A.Q.M.:A linearly implicit predictor-corrector method for reaction difusion equations. J. Comput. Math. Appl. 38, 207-216 (1999)
41. Yang, Q., Turner, I., Liu, F., Ilic, M.:Novel numerical methods for solving the time-space fractional difusion equation in 2D. SIAM J. Sci. Comput. 33, 1159-1180 (2011)
42. Zhuang, P., Liu, F., Anh, V., Turner, I.:Numerical methods for the variable-order fractional advection-difusion equation with a nonlinear source term. SIAM J. Numer. Anal. 47, 1760-1781 (2009)
