A New Efficient Method for Solving System of Weakly Singular Fractional Integro-Differential Equations by Shifted Sixth-Kind Chebyshev Polynomials

Abstract

In this paper, a new approach for solving the system of fractional integro-differential equation with weakly singular kernels is introduced. The method is based on a class of symmetric orthogonal polynomials called shifted sixth-kind Chebyshev polynomials. First, the operational matrices are constructed, and after that, the method is described. This method reduces a system of weakly singular fractional integro-differential equations (WSFIDEs) by the collocation method into a system of algebraic equations. Thereupon, an upper error bound for the proposed method is determined. Finally, some numerical examples are prepared to test the accuracy and efficiency of the presented method.