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.

Keywords

• Mixed partial derivative terms
• Operational matrices
• Legendre polynomials
• Caputo derivative
• Multi-term and Multi-order Fractional partial differential equations