References
- Ahmed E, Elgazzar AS. On fractional order differential equations model for nonlocal epidemics. Physica A:Statistical Mechanics and its Applications. 2007;379(2):607–614.
- Sun H, Chen D, Zhang Y, et al. Understanding partial bed-load transport: experiments and stochastic model analysis. J Hydrol (Amst). 2015;521:196–204.
- Chen W, Sun H, Zhang X, et al. Anomalous diffusion modeling by fractal and fractional derivatives. Comput Math Appl. 2010;59(5):1754–1758.
- Sun H, Chen W, Chen Y. Variable-order fractional differential operators in anomalous diffusion modeling. Phys A. 2009;388(21):4586–4592.
- Kilbas A, Srivastava H, Trujillo J. Theory and application of fractional differential equations. New York (NY): Elsevier Science B.V.; 2006.
- Rossikhin Y, Shitikova M. Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems. Acta Mech. 1997;120(1):109–125.
- Chen W. A speculative study of 2/3-order fractional Laplacian modeling of turbulence: some thoughts and conjectures. Chaos. 2006;16(2):023126.
- Agarwal R, Benchohra M, Hamani S. Boundary value problems for differential inclusions with fractional order. Adv Stud Contemp Math. 2008;12(2):181–196.
- Miller K, Ross B. An introduction to the fractional calculus and fractional differential equations. New York: Wiley; 1993.
- Podlubny I. Fractional differential equations. New York: Academic Press; 1998.
- Shah A, Khan R, Khan A, et al. Investigation of a system of nonlinear fractional order hybrid differential equations under usual boundary conditions for existence of solution. Math Methods Appl Sci. 2021;44(2):1628–1638.
- Tajadodi H, Khan Z, Irshad A, et al. Exact solutions of conformable fractional differential equations. Res Phys. 2021;22:1–6.
- Alshehri M, Duraihem F, Alalyani A, et al. A caputo (discretization) fractional-order model of glucose–insulin interaction: numerical solution and comparisons with experimental data. J Taibah Univ Sci. 2021;15(1):26–36.
- Bhrawy A, Zaky M. A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients. Math Methods Appl Sci. 2016;39(7):1765–1779.
- Mokhtaryand P, Ghoreishi F, Srivastava H. The Müntz-Legendre Tau method for fractional differential equations. Appl Math Model. 2016;40(2):671–684.
- Talib I, Belgacem FB, Asif NA, et al. On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions. In: AIP Conference Proceedings. Vol. 1798, No. 1. AIP Publishing; 2017.
- Khan RA, Khalil H. A new method based on Legendre polynomials for solution of system of fractional order partial differential equations. Int J Comput Math. 2014;91(12):2554–2567.
- Talib I, Tunc C, Noor ZA. New operational matrices of orthogonal Legendre polynomials and their operational. J Taibah Univ Sci. 2019;13(1):377–389.
- Doha E, Bhrawy A, Ezz-Eldien S. A new Jacobi operational matrix: an application for solving fractional differential equations. Appl Math Model. 2012;36(10):4931–4943.
- El-Sayed A, Baleanu D, Agarwal P. A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations. J Taibah Univ Sci. 2020;14(1):963–974.
- Heydari M, Atangana A, Avazzadeh Z, et al. An operational matrix method for nonlinear variable-order time fractional reaction diffusion equation involving Mittag–Leffler kernel. Eur Phys J Plus. 2020;135:237.
- Pak S, Choi H, Sin K, et al. Analytical solutions of linear inhomogeneous fractional differential equation with continuous variable coefficients. Adv Differ Equ. 2019;2019(256):1–22.
- Attar RE. Special functions and orthogonal polynomials. New York: Lulu Press; 2006.
- Mohammadi F, Hosseini M. A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations. J Franklin Inst. 2011;348(8):1787–1796.
- Saadatmandi A, Dehghan M. Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the Tau method. Commun Numer Methods Eng. 2008;24(11):1467–1474.