Open Access

ARTICLE

An Efficient Approach for Solving One-Dimensional Fractional Heat Conduction Equation

Iqbal M. Batiha^1,2,*, Iqbal H. Jebril¹, Mohammad Zuriqat³, Hamza S. Kanaan⁴, Shaher Momani^5,*

1 Department of Mathematics, Al Zaytoonah University of Jordan, Amman, 11733, Jordan
2 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates
3 Department of Mathematics, Al al-Bayt University, Mafraq, 130095, Jordan
4 Department of Mathematics, Irbid National University, Irbid, 2600, Jordan
5 Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

* Corresponding Authors: Iqbal M. Batiha. Email: ; Shaher Momani. Email:

(This article belongs to the Special Issue: Computational and Numerical Advances in Heat Transfer: Models and Methods I)

Frontiers in Heat and Mass Transfer 2023, 21, 487-504. https://doi.org/10.32604/fhmt.2023.045021

Received 15 August 2023; Accepted 25 September 2023; Issue published 30 November 2023

Abstract

Several researchers have dealt with the one-dimensional fractional heat conduction equation in the last decades, but as far as we know, no one has investigated such a problem from the perspective of developing suitable fractionalorder methods. This has actually motivated us to address this problem by the way of establishing a proper fractional approach that involves employing a combination of a novel fractional difference formula to approximate the Caputo differentiator of order α coupled with the modified three-point fractional formula to approximate the Caputo differentiator of order 2α, where 0 < α ≤ 1. As a result, the fractional heat conduction equation is then reexpressed numerically using the aforementioned formulas, and by dividing the considered mesh into multiple nodes, a system is generated and algebraically solved with the aid of MATLAB. This would allow us to obtain the desired approximate solution for the problem at hand.

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Keywords

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