Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics

Authors

  • K. Issa Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin, Nigeria
  • R. A. Bello Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin, Nigeria
  • M. H. Sulaiman Department of Mathematics and Statistics, Kwara State University, Malete, Kwara State, P. M. B. 1530, Ilorin, Nigeria

Keywords:

Iterative method, Gamma function, Parabolic equation

Abstract

In this paper, we studied and analysed a new iterative method for solving time-fractional non-linear equations by obtaining approximate solutions to the Allen-Cahn, Newell-Whitehead, and Fisher equations by putting the parameter \alpha = 1 and varying the values of \gamma, \phi, and \tau. These three equations were derived from the general non-linear dynamical wave equations when the constants therein assumed certain specific values. Obviously, from the tabulated results, we observed that the approximate solution for each example compares favourably with the existing results in the literature; therefore, the proposed scheme is effective and accurate in solving Allen-Cahn, Newell-Whitehead, and Fisher equations. All the computational work was done using Mathematica, and all the graphs were plotted using MATLAB.

Dimensions

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Published

2024-05-31

How to Cite

Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics. (2024). African Scientific Reports, 3(2), 176. https://doi.org/10.46481/asr.2024.3.2.176

Issue

Volume 3, Issue 2, August 2024 (In Progress)

Section

MATHEMATICAL SCIENCES SECTION
Copyright & Licensing

Copyright (c) 2024 K. Issa, R. A. Bello, M. H. Sulaiman

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Approximate solution of time-fractional non-linear parabolic equations arising in Mathematical Physics. (2024). African Scientific Reports, 3(2), 176. https://doi.org/10.46481/asr.2024.3.2.176