Homotopy Perturbation Method for a System of Fractal Schrödinger-Korteweg Vries Equations

Abstract

This paper presents a novel application of the Homotopy Perturbation Method (HPM) to a system of coupled fractal Schr & ouml;dinger-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.