An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations

Abstract

This paper aims to construct a general formulation for the Jacobi operational matrix of fractional integral operator. Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. Therefore, a reliable and efficient technique for the solution of them is too important. For the concept of fractional derivative we will adopt Caputo’s definition by using Riemann–Liouville fractional integral operator. Our main aim is to generalize the Jacobi integral operational matrix to the fractional calculus. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. The method is applied to solve linear and nonlinear fractional differential equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.