1. Abd-Elhameed, W.M., Doha, E.H., Youssri, Y.H., and Bassuony, M.A. New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations, Numer. Methods Partial Differ. Equ. 32(6) (2016), 1553–1571.
2. Atangana, A. and Alabaraoye, E. Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations, Adv. Differ. Equ. 2013(1) (2013), 94.
3. Bhrawy, A.H. A Jacobi spectral collocation method for solving multidimensional nonlinear fractional sub-diffusion equations, Numer. Algor. 73 (2015) 91–113.
4. Bhrawy, A.H. A space-time collocation scheme for modified anomalous subdiffusion and nonlinear superdiffusion equations, Eur. Phys. J. Plus. 82 (2016) 12 pp.
5. Bhrawy, A.H. and Zaky, M.A. A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients, Math. Methods Appl. Sci. 39(7) (2016) 1765–1779.
6. Bhrawy, A.H. and Zaky, M.A. Numerical algorithm for the variable-order Caputo fractional functional differential equation, Nonlinear Dyn. 85(3) (2016) 1815–1823.
7. Doha, E.H.On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials, J. Phys. A 37 (3) (2004), 657–675.
8. Doha, E.H., Abd-Elhameed, W.M., and Youssri, Y.H. Fully Legendre spectral Galerkin algorithm for solving linear one-dimensional telegraph type equation, Int. J. Comput. Methods, 16(8) (2019), 1850118, 19 pp.
9. Doha, E.H., Bhrawy, A.H., Baleanu, D., and Hafez, R.M. A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations, Appl. Numer. Math. 77 (2014) 43–54.
10. Doha, E.H., Bhrawy, A.H., and Ezz-Eldien, S.S. Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations, Appl. Math. Model. 35 (2011) 5662–5672.
11. Doha, E.H., Hafez, R.M., and Youssri, Y.H. Shifted Jacobi spectral Galerkin method for solving hyperbolic partial differential equations, Com put. Math. Appl. 78(3) (2019), 889–904.
12. Giona, M. and Roman, H.E. Fractional diffusion equation for transport phenomena in random media, Phys. A., 185 (1992), 87–97.
13. Hafez, R.M., Abdelkawy, M.A., Doha, E.H., and Bhrawy, A.H. A new collocation scheme for solving hyperbolic equations of second order in a semi-infinite domain, Rom. Rep. Phys. 68 (2016), 112–127.
14. Hafez, R.M., Ezz-Eldien, S.S., Bhrawy, A.H., Ahmed, E.A., and Baleanu, D. A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations, Nonlinear Dyn. 82 (2015) 1431–1440.
15. Hafez, R.M. and Youssri, Y.H. Jacobi spectral discretization for nonlinear fractional generalized seventh-order KdV equations with convergence analysis, Tbil. Math. J. 13(2) (2020) 129–148.
16. Hariharan, G., Rajaraman, R., and Mahalakshmi, M. Wavelet method for a class of space and time fractional telegraph equations, Inter. J. Phys. Sci. 7 (2012) 1591–1598.
17. Hilfer, R. Applications of fractional calculus in physics, Word Scientific, Singapore, (2000).
18. Hosseini, V.R., Chen, W., and Avazzadeh, Z. Numerical solution of fractional telegraph equation by using radial basis functions, Eng. Anal. Bound. Elem. 38 (2014) 31–39.
19. Kirchner, J.W., Feng, X., and Neal, C. Fractal stream chemistry and its implications for contaminant transport in catchments, Nature, 403 (2000), 524–526.
20. Magin, R.L. Fractional calculus in bioengineering, Begell House Publishers, 2006.
21. Meerschaert, M.M. and Tadjeran, C. Finite difference approximations for two-sided spacefractional partial differential equations, Appl. Numer. Math., 56 (2006), 80–90.
22. Miller, K. and Ross, B. An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons Inc., New York, 1993.
23. Mirzaee, F. and Samadyar, N. Numerical solution of time fractional stochastic Korteweg–de Vries equation via implicit meshless approach, Iran. J. Sci. Technol. Trans. A Sci. 43(6) (2019), 2905–2912.
24. Mirzaee, F. and Samadyar, N. Explicit representation of orthonormal Bernoulli polynomials and its application for solving Volterra–Fredholm–Hammerstein integral equations, SeMA J. 77(1) (2020), 81–96.
25. Podluny, I. Fractional differential equations Academic Press, San Diego, (1999).
26. Sweilam, N.H., Nagy, A.M., and El-Sayed, A.A. Solving time-fractional order telegraph equation via sinc-Legendre collocation method, Mediterr. J. Math., 13 (2016) 5119–5133.
27. Wei, L., Dai, H., Zhang, D., and Si, Z. Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation, Calcolo, (2014) 51 175–192.
28. Yildirim, A. He’s homotopy perturbation method for solving the space and time-fractional telegraph equations, Inter. J. Comput. Math. 87 ( 2010) 2998–3006.
29. Youssri, Y.H. and Abd-Elhameed, W.M. Numerical spectral Legendre Galerkin algorithm for solving time fractional Telegraph equation, Rom. J. Phys. 63(107) (2018), 1–16.
30. Zayernouri, M., Ainsworth, M., and Karniadakis, G.E. A unified Petrov Galerkin spectral method for fractional PDEs, Comp. Methods Appl. Mech. Eng. 283 (2015) 1545–1569.
