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ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Mathematical Physics
Volume 11 - 2025 | doi: 10.3389/fams.2025.1568757
Application of the Tanh-Coth and HSI methods in deriving exact analytical solutions for the STFKS Equation
Provisionally accepted
Abaker A. Hassaballa1
Elzain E. A. Gumma2*Ahmed M. A. Adam2Omer M. A. Hamed3
Ali Satty2
Mohyaldein Salih2Faroug A. Abdalla4
Zakariya Mohammed1- 1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, Northern Borders, Saudi Arabia
- 2Department of Mathematics, Northern Border University, Arar, Saudi Arabia
- 3Department of Finance and Insurance, Northern Border University, Arar, Saudi Arabia
- 4Department of Computer Science, Northern Border University, Arar, Saudi Arabia
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This article utilizes the Tanh-Coth and He's Semi-Inverse (HSI) methods to obtain solitary wave solutions for the stochastic time Fractional Kuramoto-Sivashinsky (STFKS) equation, applying the Truncated M-fractional derivative (TMFD) technique. The main objective is to derive traveling wave solutions for the STFKS equation. Graphical representations are provided to illustrate the physical properties of these solutions. The Tanh-Coth and HSI methods are validated as robust and efficient approaches for solving the STFKS equation.
Keywords: nonlinear partial differential equation, Stochastic time fractional Kuramoto-Sivashinsky equation, Truncated M-fractional derivative, Tanh-coth method, He's Semi-Inverse methods
Received: 30 Jan 2025; Accepted: 14 Apr 2025.
Copyright: © 2025 Hassaballa, Gumma, Adam, Hamed, Satty, Salih, Abdalla and Mohammed. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Elzain E. A. Gumma, Department of Mathematics, Northern Border University, Arar, Saudi Arabia
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