A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations

Abstract

Our main aim in this work is to find the operational matrix of fractional derivative and the operational matrix of distributed order fractional derivative for the Müntz–Legendre polynomials (MLPs). The operational matrix approach with the tau method or collocation method is applied to reduce the solution of the linear/nonlinear distributed order fractional differential equations (DFDEs) to a system of linear/nonlinear algebraic equations. Moreover, seven numerical examples are included to show the validity and applicability of the suggested methods.