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

Iqbal M. Batiha1,2,*, Iqbal H. Jebril1, Mohammad Zuriqat3, Hamza S. Kanaan4, Shaher Momani5,*

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: email; Shaher Momani. Email: email

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

Frontiers in Heat and Mass Transfer 2023, 21, 487-504.


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.


Cite This Article

Batiha, I. M., Jebril, I. H., Zuriqat, M., Kanaan, H. S., Momani, S. (2023). An Efficient Approach for Solving One-Dimensional Fractional Heat Conduction Equation. Frontiers in Heat and Mass Transfer, 21(1), 487–504.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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