The operational matrix of fractional integration for shifted Legendre polynomials

Document Type: Regular Paper


Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 74811-71466, Shiraz, Iran


In this article we implement an operational matrix of fractional integration for Legendre polynomials. We proposed an algorithm to obtain an approximation solution for fractional differential equations, described in Riemann-Liouville sense, based on shifted Legendre polynomials. This method was applied to solve linear multi-order fractional differential equation with initial conditions, and the exact solutions obtained for some illustrated examples. Numerical results reveal that this method gives ideal approximation for linear multi-order fractional differential equations.