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The New Analysis Of Fractional-Order Multi-Dimensional Diffusion Equations By Zz Transform With Mittag-Leffler Kernel

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nehad Ali Shah & Mohammed Kbiri Alaoui & Ali Akgul & Ahmed M. Zidan & Jae Dong Chung, 2023. "The New Analysis Of Fractional-Order Multi-Dimensional Diffusion Equations By Zz Transform With Mittag-Leffler Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-22.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23400819
    DOI: 10.1142/S0218348X23400819
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