1. Badakhshan, K. P. and Kamyad, A. V. Numerical solution of nonlinea optimal control problems using nonlinear programming, Appl. Math. Com put., 187 (2007), 1511–1519.
2. Bhrawy, A. H., Doha, E. H., Tenreiro Machado, J. A. and Ezz-Eldien, S. S An Efficient Numerical Scheme for Solving Multi-Dimensional Fractiona Optimal Control Problems With a Quadratic Performance Index, Asian J Control 17(2015), no. 6, 2389–2402
3. Bhrawy, A. H., Zaky, M. A. and Machado, J. T. Efficient Legendre spec tral tau algorithm for solving the two-sided space-time Caputo fractiona advection-dispersion equation, J. Vib. Control, 22 (2016), no. 8, 2053–2068.
4. Blank, L. Numerical treatment of differential equations of fractional order Nonlinear World 4 (1997), no. 4, 473–491.
5. Deng, W. Finite element method for the space and time fractional Fokker Planck equation, SIAM J. Numer. Anal. 47 (2008/09), no. 1, 204–226.
6. Folland, G. B. Real analysis: modern techniques and their applications, John Wiley & Sons, 2013.
7. Ford, N. J., Xiao, J. and Yan , Y. A finite element method for time frac tional partial differential equations, Fract. Calc. Appl. Anal. 14 (2011), no. 3, 454–474.
8. Ghandehari, M. A. M. and Ranjbar, M. A numerical method for solving a fractional partial differential equation through converting it into an NLP problem, Comput. Math. Appl. 65 (2013), no. 7, 975–982.
9. Huang, G., Huang, Q. and Zhan, H. Evidence of one-dimensional scale dependent fractional advection-dispersion, J. contam. hydro. 85 (2006), 53–71.
10. Irandoust-pakchin, S., Dehghan, M., Abdi-mazraeh, S. and Lakestani, M. Numerical solution for a class of fractional convection-diffusion equations using the flatlet oblique multiwavelets, J. Vib. Control 20(2014), no. 6, 913–924.
11. Jafari, H. and Tajadodi, H. Numerical solutions of the fractional advection-dispersion equation, Progr. Fract. Differ. Appl. 1, (2015), No. 1, 37–45.
12. Jia, J. and Wang, H. Fast finite difference methods for space-fractional diffusion equations with fractional derivative boundary conditions, J. Compu. Phys. 293 (2014), 359–369.
13. Kilbas, A. A. A., Srivastava, H. M. and Trujillo, J. J. Theory and ap plications of fractional differential equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
14. Kiryakova, V. S. Generalized fractional calculus and applications, Pitman Research Notes in Mathematics Series, 301. Longman Scientific & Tech nical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
15. Langlands, T. A. M. and Henry, B. I. The accuracy and stability of an implicit solution method for the fractional diffusion equation, J. Comput. Phys. 205 (2005), 719–736.
16. Lin, Y. and Xu, C. Finite difference/spectral approximations for the time fractional diffusion equation, J. Comput. Phys. 225 (2007), 1533–1552.
17. Liu, F., Anh, V. and Turner, I. Numerical solution of the space fractional Fokker-Planck equation, J. Comput. Appl. Math. 166 (2004), 209–219.
18. Momani, S. and Odibat, Z. Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method, Appl. Math. Comput. 177 (2006), 488–494.
19. Odibat, Z. M. and Momani, S. Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlin. Sci. Num. Simul. 7 (2006), 27–34.
20. Odibat, Z. and Momani, S. An algorithm for the numerical solution of differential equations of fractional order, J. Appl. Math. Inform, 26 (2008), 15–27.
21. Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic press, 198 1998.
22. Podlubny, I. Matrix approach to discrete fractional calculus, Fract. Calc. Appl. Anal. 3 (2000), 359–386.
23. Podlubny, I., Chechkin, A., Skovranek, T., Chen, Y. and Jara, B. M. V. Matrix approach to discrete fractional calculus II: Partial fractional differential equations, J. Comput. Phys. 228 (2009), 3137–3153.
24. Rudin, W. Real and complex analysis, Tata McGraw-Hill Education, 1987.
25. Shen, S., Liu, F., Anh, V. and Turner, I. The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation, IMA J. Appl. Math. 73 (2008), 850–872.
26. Sun, Z. and Wu, X. A fully discrete difference scheme for a diffusion-wave system, Appl. Numer. Math. 56 (2006), 193–209.
27. Tricaud, C. and Chen, Y. Q. An approximate method for numerically solving fractional order optimal control problems of general form, Comput. Math. Appl. 59 (2010), 1644–1655.
28. Zeid, S. S., Kamyad, A. V., Effati, S., Rakhshan, S. A. and Hosseinpour, S. Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach, SeMA J. 74 (2017), 585–603.
29. Zhao, L. and Deng, W. Jacobian-predictor-corrector approach for fractional differential equations, Adv. Comput. Math. 40 (2014), 137–165.
30. Zhang, Y. Finite difference approximations for space-time fractional partial differential equation, J. Numer. Math. 17 (2009), 319–326.
