A COMPARATIVE STUDY OF SEMI-ANALYTICAL METHODS FOR SOLVING FRACTIONAL-ORDER CAUCHY REACTION–DIFFUSION EQUATION

Yu-Ming Chu, Nehad Ali Shah, Hijaz Ahmad, Jae Dong Chung () and S. M. Khaled ()
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Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China2Hunan Provincial Key Laboratory of Mathematical Modeling, Analysis in Engineering, Changsha, University of Science & Technology, Changsha 410114, P. R. China
Nehad Ali Shah: Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam4Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Hijaz Ahmad: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
S. M. Khaled: Department of Mathematics, Faculty of Science, Helwan University, P. O. Box 11795, Cairo, Egypt

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-15

Abstract: In this paper, the Homotopy perturbation transform method and New Iterative transform method are implemented to evaluate the time-fractional Cauchy reaction–diffusion equation’s solution. In this method, Elzaki transform is combined with the Homotopy perturbation method and New Iteration method. Four problems are investigated to show, demonstrate and validate the efficacy of the current technique. The analytical results achieved by the current technique indicate that the approach is easy to implement and accurate. These solutions reveal that the suggested method is very useful and straightforward to perform the problems of engineering sciences.

Keywords: Homotopy Perturbation Method; New Iterative Method; Elzaki Transform; Caputo Derivatives; Cauchy Reaction–Diffusion Equation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501437

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