Numerical Solution of Fractional Differential Equation System Using the Muntz-Legendre Polynomials

Abstract

Abstract:In the paper, we apply a numerical approach to approximate solution of a system of the fractional differential equations based on the Müntz-Legendre polynomials.Features of these polynomials make them so appropriate for solving the fractional differential equation system. In the proposed method, a system of the fractional differential equations is transformed into a system of the algebraic equations which is move easier to solve. The numerical examples show accuracy and convergence of the present method.

An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences

“…Additionally, Singh et al [25] have presented the analysis of coupled fractional Burger's equations by employing a homotopy technique. In 2017, FPDEs have been handled by using Muntz-Legendre polynomial approach [26], fractional complex differential transform scheme [27], and two-dimensional Laplace transform [28]. Recently the FPDEs with Caputo-Fabrizio fractional operator have been investigated through HPTM by Gomez-Aguilar et al [29].…”