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

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 computat...

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Published in:Alexandria engineering journal 2022-01, Vol.61 (1), p.135-145
Main Authors: Talib, Imran, Jarad, Fahd, Mirza, Muhammad Umar, Nawaz, Asma, Riaz, Muhammad Bilal
Format: Article
Language:English
Subjects:
Caputo derivative
Legendre polynomials
Mixed partial derivative terms
Multi-term and Multi-order Fractional partial differential equations
Operational matrices
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description 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.
doi_str_mv 10.1016/j.aej.2021.04.067
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subjects Caputo derivative
Legendre polynomials
Mixed partial derivative terms
Multi-term and Multi-order Fractional partial differential equations
Operational matrices
title A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
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