THE NEW ANALYSIS OF FRACTIONAL-ORDER MULTI-DIMENSIONAL DIFFUSION EQUATIONS BY ZZ TRANSFORM WITH MITTAG-LEFFLER KERNEL

Nehad Ali Shah (), Mohammed Kbiri Alaoui (), Ali Akgul (), Ahmed M. Zidan () and Jae Dong Chung
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Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Mohammed Kbiri Alaoui: ��Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Ali Akgul: ��Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Ahmed M. Zidan: ��Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-22

Abstract: In this paper, two well-known analytic approaches for solving diffusion equations are implemented. We propose a modified version of the homotopy perturbation method and Adomian decomposition methods utilizing the ZZ transform. In this sense, the fractional derivative of the Atangana–Baleanu derivative is provided. In addition, concrete examples are as well provided to demonstrate the precision of the proposed methodologies. The proposed solution is observed to have the desired rate of convergence towards the exact answer. The key advantage of the proposed method is the small amount of calculations. To demonstrate the validity of the suggested methods, we give graphical representation of analytical and exact solutions that are in close contact.

Keywords: ZZ Transform; Homotopy Perturbation Method; Modified Decomposition Method; Atangana–Baleanu Derivative; Diffusion Equations (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400819

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