Homotopy-Sumudu transforms for solving system of fractional partial differential equations
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(2020) 2020:222
RESEARCH
Open Access
Homotopy-Sumudu transforms for solving system of fractional partial differential equations A.K. Alomari1* *
Correspondence: [email protected] 1 Department of Mathematics, Yarmouk University, Irbid, Jordan
Abstract In this paper, we investigate the Sumudu transforms and homotopy analysis method (S-HAM) for solving a system of fractional partial differential equations. A general framework for solving such a kind of problems is presented. The method can also be utilized to solve systems of fractional equations of unequal orders. The algorithm is reliable and robust. Existence and convergence results concerning the proposed solution are given. Numerical examples are introduced to demonstrate the efficiency and accuracy of the algorithm. Keywords: Fractional system of PDEs; Coupled Burger’s equation; Sumudu transform; Fractional calculus; Homotopy analysis method
1 Introduction The fractional differential equation (FDE) is one of the most important topics in the recent years, not only because it can be used for modeling real-life phenomena, but also it gives researchers a wide range as regards the material properties. The fractional-order models are more adequate than the previously used integer-order models [1, 2], because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. A system of fractional partial differential equations is a tool with impact on modeling several phenomena in different fields, such as fluid mechanic, biology, finance and material science. Finding the exact solution for a FDE is very difficult even for a the linear one, so approximate solutions are needed. The solution of the system of fractional partial differential equations was pointed out by several researchers such as Ertürk and Momani who applied the differential transform method [3]. Ghazanfari investigated the fractional complex transform method [4]. Jafari et al. presented a Laplace transform with the iterative method [5]. Ahmed et al. used the Laplace Adomian decomposition method and the Laplace variational iteration method [6]. Homotopy analysis method is one of the most effective methods for solving FDE [7, 8]. It can give a convergent series solution that depends on a convergent control parameter, and the series can be represented using various basis functions. The major drawback of the © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted
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