https://doi.org/10.1140/epjs/s11734-025-01807-5
Regular Article
Homotopy perturbation method for a system of fractal Schrödinger–Korteweg–de Vries equations
1
Department of Physics, Ur.C., Islamic Azad University, 63896, Urmia, West Azerbaijan, Iran
2
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey
3
Department of Biology, University of Texas at Arlington, 76019, Arlington, TX, USA
4
Department of Mathematics, University of Texas at San Antonio, 78249, San Antonio, TX, USA
5
Universität Duisburg-Essen, Fakultät für Mathematik, Nichtlineare Optimierung, Thea-Leymann-Straße 9, 45127, Essen, Germany
6
Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
a alireza.khalili@iau.ac.ir, alirezakhalili@yyu.edu.tr
Received:
11
March
2025
Accepted:
12
July
2025
Published online:
22
July
2025
This paper presents a novel application of the Homotopy Perturbation Method (HPM) to a system of coupled fractal Schrödinger–Korteweg–de Vries (S-KdV) equations, formulated within the framework of fractal calculus. By extending classical S-KdV equations and diffusion–reaction systems to fractal space, we introduce a new mathematical model that captures the complex behavior of nonlinear wave interactions and reaction–diffusion processes in media with fractal geometries. The main contribution of this work lies in deriving approximate analytical solutions for these fractal systems using HPM, demonstrating both its effectiveness and accuracy in handling fractal differential equations. The influence of fractal time and space on the system dynamics is examined and visualized through detailed graphical analysis. This study provides a foundation for further exploration of fractal models in physical and engineering contexts, offering insights into how fractality alters classical system behavior.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
