Abstract
This paper introduces a new numerical approach to solving a system of fractional differential equations (FDEs) using the Legendre wavelet operational matrix method (LWOMM). We first formulated the operational matrix of fractional derivatives in some special conditions using some notable characteristics of Legendre wavelets and shifted Legendre polynomials. Then, the system of fractional differential equations was transformed into a system of algebraic equations by using these operational matrices. At the end of this paper, several examples are presented to illustrate the effectivity and correctness of the proposed approach. Comparing the methodology with several recognized methods demonstrates that the advantages of the Legendre wavelet operational matrix method are its accuracy and the understandability of the calculations.
Highlights
Differential and integral operators are the basis of mathematical models, and they are used as a means of understanding the working principles of natural and artificial systems
This paper focuses on the numerical analysis of a system of fractional order differential equations using the Legendre wavelet operational matrix method
We considered the following nonlinear system of fractional differential equations with the initial conditions [8]
Summary
Differential and integral operators are the basis of mathematical models, and they are used as a means of understanding the working principles of natural and artificial systems. Because a variety of solutions of fractional differential equations (FDEs) cannot be found analytically, numerical and approximate methods are needed. There are a lot of techniques that have been studied by many researchers in solving FDEs and the system of such equations numerically Some of these techniques are the Adomian decomposition method presented by Song and Wang [1], the collocation method, the improved operational matrix method [2,3,4], the perturbation iteration method introduced by. This paper focuses on the numerical analysis of a system of fractional order differential equations using the Legendre wavelet operational matrix method.
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