The Construction of Operational Matrix of Fractional Integration Using the Fractional Chebyshev Polynomials

Abstract

In this paper we present a computational method for solving generalized Abel integral equations. To this end, first, a new operational matrix of fractional order integration for fractional Chebyshev polynomials is derived. The error analysis of the proposed method is studied theoretically. Then, by applying this matrix, collocation and Galerkin methods, we reduce the original problem to a linear system of algebraic equations. Finally, comparison of numerical results with the exact solution shows the validity and efficiency of the presented method.