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Open AccessFeature PaperArticle
Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function
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Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2
IT4Innovations, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic
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Department of Computer Science and Mathematics, Lebanese American University, Byblos 1102 2801, Lebanon
4
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(13), 2137; https://doi.org/10.3390/math12132137 (registering DOI)
Submission received: 3 June 2024
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Revised: 27 June 2024
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Accepted: 3 July 2024
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Published: 7 July 2024
Abstract
Fractional differential equations play a significant role in various scientific and engineering disciplines, offering a more sophisticated framework for modeling complex behaviors and phenomena that involve multiple independent variables and non-integer-order derivatives. In the current research, an effective cubic B-spline collocation method is used to obtain the numerical solution of the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. It is implemented with the help of a -weighted scheme to solve the proposed problem. The spatial derivative is interpolated using cubic B-spline functions, whereas the temporal derivative is discretized by the Atangana–Baleanu operator and finite difference scheme. The proposed approach is stable across each temporal direction as well as second-order convergent. The study investigates the convergence order, error norms, and graphical visualization of the solution for various values of the non-integer parameter. The efficacy of the technique is assessed by implementing it on three test examples and we find that it is more efficient than some existing methods in the literature. To our knowledge, no prior application of this approach has been made for the numerical solution of the given problem, making it a first in this regard.
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MDPI and ACS Style
Hayat, A.M.; Riaz, M.B.; Abbas, M.; Alosaimi, M.; Jhangeer, A.; Nazir, T.
Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function. Mathematics 2024, 12, 2137.
https://doi.org/10.3390/math12132137
AMA Style
Hayat AM, Riaz MB, Abbas M, Alosaimi M, Jhangeer A, Nazir T.
Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function. Mathematics. 2024; 12(13):2137.
https://doi.org/10.3390/math12132137
Chicago/Turabian Style
Hayat, Afzaal Mubashir, Muhammad Bilal Riaz, Muhammad Abbas, Moataz Alosaimi, Adil Jhangeer, and Tahir Nazir.
2024. "Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function" Mathematics 12, no. 13: 2137.
https://doi.org/10.3390/math12132137
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