AccScience Publishing / NSCE / Online First / DOI: 10.36922/NSCE026120009
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RESEARCH ARTICLE

Characterization of solitary wave dynamics in the nonlinear fractional Allen–Cahn model via two consistent analytical schemes

Md. Mizanur Rahman1* ,  Md. Al-Amin1 ,  Md. Shajib Ali1 ,  Md. Nurul Islam1 ,  Md. Ali Akbar2
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1 Department of Mathematics, Faculty of Science, Islamic University, Kushtia, Khulna, Bangladesh
2 Department of Applied Mathematics, Faculty of Science, University of Rajshahi, Rajshahi, Bangladesh
NSCE 2026, 2(2), 026120009 https://doi.org/10.36922/NSCE026120009
Received: 20 March 2026 | Revised: 29 April 2026 | Accepted: 18 May 2026 | Published online: 26 June 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

In this study, we aim to construct exact solitary-wave solutions of the time-fractional Allen–Cahn (AC) model using the conformable derivative framework. The AC model is effective for describing various physical phenomena, such as the mixing of two incompressible fluids, the motion of phase boundaries in crystalline solids, solid nucleation, vesicle membranes, and phase separation in iron alloys, among others. We initially identify the soliton solutions of the model under consideration using the generalized exponential rational function method and the improved modified simplest equation method. When applied with appropriate parameter values, the considered methods can generate trigonometric, hyperbolic, complex hyperbolic, rational, and mixed-type solutions via fractional wave transformation. The employed methods incorporate multiple parameters that can be varied to modify the properties of the resulting solutions. These results enhance our theoretical understanding of complex nonlinear systems and demonstrate the potential applications of advanced mathematical methods. Additionally, we analyze the influence of the fractional-order parameter on the obtained results using graphical visualization to reveal the underlying dynamics of the related phenomenon. We also perform a stability analysis of the model under consideration and critically assess the novelty of this study relative to the existing literature. The attained results demonstrate the effectiveness and robustness of the employed methods.

Keywords
Generalized exponential rational function method
Improved modified simplest equation method
Time-fractional Allen–Cahn model
Solitons
Funding
None.
Conflict of interest
There is no conflict of interest.
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