Differential transform method with complex transforms to some nonlinear fractional problems in mathematical physics
type: Item
instance of: scholarly article
title: Differential transform method with complex transforms to some nonlinear fractional problems in mathematical physics
zbMATH Open document ID: 1394.35560
DOI: 10.1155/2015/364853
author: Syed Tauseef Mohyud-Din
author: Farah Jabeen Awan
author: Jamshad Ahmad
author: Saleh M. Hassan
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie's sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian's polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6926154
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/364853
OpenAlex ID: W2188460738
Wikidata QID: Q59118172
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description: scientific article; zbMATH DE number 6926154