New homotopy analysis transform method for solving multidimensional fractional diffusion equations

In this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the...

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Bibliographic Details
Published in:	Arab journal of basic and applied sciences Vol. 27; no. 1; pp. 27 - 44
Main Authors:	Maitama, Shehu, Zhao, Weidong
Format:	Journal Article
Language:	English
Published:	Taylor & Francis 01.01.2020 Taylor & Francis Group
Subjects:	fractional diffusion equations homotopy analysis Shehu transform method Shehu transform method symbolic-numeric computation
ISSN:	2576-5299, 2576-5299
Online Access:	Get full text
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Summary:	In this paper, we introduce a new semi-analytical method called the homotopy analysis Shehu transform method (HASTM) for solving multidimensional fractional diffusion equations. The proposed technique is a combination of the homotopy analysis method and the Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms. Shehu transform is user-friendly, and its visualization is easier than the Sumudu, and the natural transforms. The convergence analysis of the method is proved, and we provide some applications of the fractional diffusion equations to validate the efficiency and the high accuracy of the technique. The results obtained using the HASTM are in complete agreement with the results of the existing techniques.
ISSN:	2576-5299 2576-5299
DOI:	10.1080/25765299.2019.1706234