A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations

Abstract

In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.