Abstract
Many conventional physical and engineering phenomena have been identified to be well expressed by making use of the fractional order partial differential equations (FOPDEs). For that reason, a proficient and stable numerical method is needed to find the approximate solution of FOPDEs. This article is designed to develop the numerical scheme able to find the approximate solution of generalized fractional order coupled systems (FOCSs) with mixed partial derivative terms of fractional order. Our main objective in this article is the development of a new operational matrix for fractional mixed partial derivatives based on the orthogonal shifted Legendre polynomials (SLPs). The fractional derivatives are considered herein in the sense of Caputo. The proposed method has the advantage to reduce the considered problems to a system of algebraic equations which are simple in handling by any computational software. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some examples are included to demonstrate the accuracy and validity of the proposed method.
Highlights
For the last few decades, the subject fractional calculus (FC) has gotten considerable attention of the researchers round the globe due to its non-local behaviour
We are eager to extend the applications of orthogonal shifted Legendre polynomials (SLPs) to solve generalized fractional order coupled systems (FOCSs) with mixed partial derivative terms of fractional order employing operational matrices approach
Our main objective in this article was the development of the new numerical method for finding the approximate solution of generalized FOCSs with mixed partial derivative terms of fractional order
Summary
For the last few decades, the subject fractional calculus (FC) has gotten considerable attention of the researchers round the globe due to its non-local behaviour. The prime idea behind the technique of applying an orthogonal basis is that it reduces the under consideration problem into a system of algebraic equations, greatly simplifying the problem and simple in handling using any computational software In this approach, a truncated orthogonal series is used for numerical integration of differential equations, with the goal of obtaining efficient computational solutions. We are eager to extend the applications of orthogonal SLPs to solve generalized FOCSs with mixed partial derivative terms of fractional order employing operational matrices approach.
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