The Analytical Solution of Nonhomogeneous Fractional Ordinary Differential Equations by the Aboodh Transform Method

Benattia ME and Belghaba K

Published on: 2020-05-31

Abstract

In this paper, We introduce the rudiments of fractional computing and the consequent applications of the Aboodh transform on fractional derivatives. Once this connection is firmly established in the general context, we turn to the application of the Aboodh transformation method (ATM) to certain interesting non-homogeneous fractional ordinary differential equations (NHFODEs). The method used here is highly efficient, powerful, and confidential tool in terms of finding exact solutions.

Keywords

Aboodh transform Fractional differential equation Riemann-Liouville fractional derivative

Introduction

Many physical problems can be described by mathematical models that involve ordinary or partial differential equations. A mathematical model is a simplified description of physical reality expressed in mathematical terms. Thus, several numerical methods were developed for solving certain fractional differential equations. There is a lot of literature available on the theory and applications of integral transforms. Integral transforms like Laplace, Fourier,Sumudu and Mellin are used in the solution of fractional differential equations. Recently, Khalid Suliman Aboodh defined a new integral transforms called Aboodh transform which applied it to solve non-homogeneous fractional differential equations [1-6].