On new aspects of Chebyshev polynomials for space-time fractional diffusion process

[1] R.L. Bagley, P.J. Torvik, Fractional calculus a different approach to the analysis of viscoelastically damped structures, AIAA J. 21 (1983) 741–748. Search in Google Scholar

[2] I. Podlubny, Fractional differential equations, vol. 198 of mathematics in science and engineering, San Diego: Academic Press, 1999. Search in Google Scholar

[3] R.P. Agarwal, M. Belmekki, M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Differ. Equ. 2009 (2009) 981728. Search in Google Scholar

[4] K.S. Hedrih, The transversal creeping vibrations of a fractional derivative order constitutive relation of nonhomogeneous beam, Math. Probl. Eng. (2006) https://doi.org/10.1155/MPE/2006/46236. Search in Google Scholar

[5] P.J. Torvik, R.L. Bagley, On the appearance of the fractional derivative in the behaviour of real materials, J. Appl. Mech. Trans. ASME 51 (1984) 294–298. Search in Google Scholar

[6] S.S. Ray, R.K. Bera, Analytical solution of the Bagley-Torvik equation by Adomian decomposition method, Appl. Math. Comput. 68 (2005) 398–410. Search in Google Scholar

[7] S. Manabe, A suggestion of fractional-order controller for flexible spacecraft attitude control, Nonlinear Dyn. 29 (2002) 251–268. Search in Google Scholar

[8] S. Das, Solution of extraordinary differential equations with physical reasoning by obtaining modal reaction series, Model. Simul. Eng. 2010 (2010). Search in Google Scholar

[9] Y. Luo, Y. Hu, Z. Lu, Analytical solution of the linear fractional differential equation by Adomian decomposition method, J. Comput. Appl. Math. 215 (2008) 220–229. Search in Google Scholar

[10] A. Ghorbani, A. Alavi, Application of He’s variational iteration method to solve semi differential equations of nth order, Math. Probl. Eng. 14 (2008) 1–10. Search in Google Scholar

[11] J. He, Approximate analytical solution for fractional derivatives in porous media, Computer Meth. in Appl. Mech. and Eng. 167(1-2)(1998) 57-68. Search in Google Scholar

[12] M. Seifollahi, A. S Shamloo, Numerical solution of non linear muti-order fractional differential equations by operational matrix of chebyshev polynomials, World Appl. Prog. 3 (2013) 85–92. Search in Google Scholar

[13] A. A. Hemeda, Homotopy Perturbation Method for Solving Partial Differential Equations of Fractional Order, Int. J. of Math. Analy. 6(49) (2012) 2431–2448. Search in Google Scholar

[14] M. M. Khadar, N. H. Sweilam, A. M. S. Mahdy, An efficient method for solving the fractional diffusion equation, Int J. Pure and Appl. Math. 1(2)(2011) 1–12. Search in Google Scholar

[15] M. M. Khader, On the numerical solutions for the fractional diffusion equation, Commun. in Nonlin. Sci. and Num. Simul. (2010) doi: 10.1016/j.cnsns.2010.09.007. Search in Google Scholar

[16] H. D. Eid , A. H. Bhrawy, D. Baleanu, S.S. Ezz-Eldien, The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation, Springer open journal, Doha et al. Adv. in diff. eq. (2014) 201–231. Search in Google Scholar

[17] A.A.A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science, 204 2006. Search in Google Scholar

[18] J. T. Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus, Commun. in Nonlin. Sci. and Num. Simul. 16(3)(2011) 1140–1153 doi:10.1016/j.cnsns.2010.05.027. Search in Google Scholar

[19] Y. Tian, A. Chen, The existence of positive solution to three-point singular boundary value problem of fractional differential equation, Abstr. Appl. Anal. 2009 314656 (2009) https://doi.org/10.1155/2009/314656. Search in Google Scholar

[20] R. Magin, X. Feng, D. Baleanu, Solving fractional order Bloch equation, Concept magnetic Res. 34A, 16-23 (2009). Search in Google Scholar

[21] J. Wu, Theory and Applications of Partial Functional Differential Equations, New York, NY, USA, Springer, 1996. Search in Google Scholar

[22] J.C. Mason, D.C. Handscomb, Chebyshev Polynomials, Chapman and Hall, New York, 2003. Search in Google Scholar

[23] P. Agarwal, A.A.El-Sayed, Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation, Physica A 500 (2018) 40-49. Search in Google Scholar

[24] Z. Odibat, D. Baleanu, A linearization-based approach of homotopy analysis method for non-linear time-fractional parabolic PDEs, Mathematical methods in the applied sciences, 42 18 (2019) 7222–7232. Search in Google Scholar

[25] S, Amiri, M. Hajipour, D. Baleanu, A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra-Fredholm integral equations, Applied Mathematics and Computation, 370 124915 (2020) 1–13. Search in Google Scholar

[26] U. Farooq, H. Khan, D. Baleanu, M. Arif, Numerical solutions of fractional delay differential equations using Chebyshev wavelet method, Computational and Applied Mathematics, 38 195 (2019) 1-13. Search in Google Scholar