GENERALIZED CAPUTO-KATUGAMPOLA FOR SOLVING FUZZY FRACTIONAL HEAT EQUATION


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Authors

  • Abdallah Alshbeel Universiti Sains Malaysia
  • Dr. Amirah School of Mathematical Sciences, Universiti Sains Malaysia
  • Dr. Abdelkareem Alomari Department of Mathematics, Faculty of Science, Yarmouk University

Abstract

The fuzzy theory is investigated in this paper and the frac-
tional derivative with two parameters is used to construct the solution
of the fuzzy fractional heat equation. We devised a method for comput-
ing a semi-analytical solution to a fuzzy fractional-order heat equation
based on the Optimal Homotopy Asymptotic Method (OHAM). This
method helps us to overcome the obstacles and constraints that other
approaches impose whereby it is used to construct powerful and efficient
ways of finding the solutions to the heat equation with more accuracy,
minimal effort, and iterations. The Mittag–Leffler (ML) kernels which
include two parameters Eσ
ν,ξ (λ, s) are utilized to define the fractional
derivative. A broad approach to dealing with this type of situation is
presented. Several examples are provided to validate the outcome, which
is then contrasted with the precise solution to demonstrate the effective-
ness and feasibility of the proposed method. The results are presented
in terms of tables and figures

Author Biographies

Dr. Amirah, School of Mathematical Sciences, Universiti Sains Malaysia

D. Amirah Azmi 
School of Mathematical Sciences, Universiti Sains Malaysia, 
Gelugor, Penang, Malaysia. 
e-mail: amirahazmi@usm.my

Dr. Abdelkareem Alomari, Department of Mathematics, Faculty of Science, Yarmouk University

A.K. Alomari 
Department of Mathematics,
Department of Mathematics, Faculty of Science, Yarmouk University, 
Irbid 211-63, Jordan. 
e-mail: abdomari2008@yahoo.com

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Published

2023-12-07

How to Cite

Alshbeel, A., AMIRAH AZMI, & A.K. Alomari. (2023). GENERALIZED CAPUTO-KATUGAMPOLA FOR SOLVING FUZZY FRACTIONAL HEAT EQUATION. Results in Nonlinear Analysis, 7(1), 44–63. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/320