Exploring the Elzaki Transform: Unveiling Solutions to Reaction-Diffusion Equations with Generalized Composite Fractional Derivatives

Authors

  • Mohd Khalid Department of Mathematics, Maulana Azad National Urdu University, Gachibowli, Hyderabad-500032, India
  • Ishfaq Ahmad Mallah Department of Mathematics, Maulana Azad National Urdu University, Gachibowli, Hyderabad-500032, India
  • Subhash Alha Department of Mathematics, Maulana Azad National Urdu University, Gachibowli, Hyderabad-500032, India
  • Ali Akgul Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey

DOI:

https://doi.org/10.37256/cm.5220244621

Keywords:

elzaki transform, generalised composite fractional derivative, reaction-diffusion equation, fourier transform, fractional calculus applications

Abstract

This article investigates the use of the Elzaki transform on a generalized composite fractional derivative. To establish the framework for this inquiry, numerous essential lemmas about the Elzaki transform are presented. We successfully extract the solution to the reaction-diffusion problem using both the Elzaki and Fourier transforms, which include a generalized composite fractional derivative. We also look at special examples of the generalized equation, which helps us understand its applications and consequences better. The results show that the Elzaki transform is successful in dealing with complicated fractional differential equations, introducing new analytical approaches and solutions to the subject of fractional calculus and its applications in reaction-diffusion systems.

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Published

2024-06-25

How to Cite

1.
Khalid M, Mallah IA, Alha S, Akgul A. Exploring the Elzaki Transform: Unveiling Solutions to Reaction-Diffusion Equations with Generalized Composite Fractional Derivatives. Contemp. Math. [Internet]. 2024 Jun. 25 [cited 2024 Dec. 11];5(2):1426-38. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4621

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