Abstract
In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.
Highlights
Over the last three decades, fractional calculus has been enormously developed and taken on in many fields of scientific research
Integro-differential equations and fractional differential systems have recently proved to be very useful in the field of physics, engineering, control processing for visco-elastic systems, diffusion
We find that many researchers have been interested in solving this kind of linear and nonlinear differential equations systems of fractional differential equations
Summary
Over the last three decades, fractional calculus has been enormously developed and taken on in many fields of scientific research. The investigation of the exact solutions to nonlinear equations play an important role in the study of nonlinear physical phenomena, the nonlinear differential equations are the most complex in the solution compared with linear differential equations Integral transformations such as Laplace, Sumudu, natural, Elzaki and Aboodh are unable to solve the nonlinear differential equations. Based on the mathematical simplicity of the Aboodh transform and its fundamental properties, Aboodh transform was introduced by Khalid Aboodh in 2013, to facilitate the process of solving ordinary and partial differential equations in the time domain This transformation has deeper connection with the Laplace and Elzaki transform [8]. The objective of this study is coupling the Adomian decompositionmethod (ADM) with Aboodh transform in the sense of fractional derivative, we apply this modified method to solve some examples related with systems of nolinear fractional partial differential equations.
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