Homotopy Perturbation Method for Fractal Differential Equations

Abstract

This paper presents the application of the Homotopy Perturbation Method (HPM) to solve both linear and nonlinear ordinary fractal differential equations. We begin with a review of fractal calculus, including the definition of a fractal Banach space and relevant fixed point theorems. The formulation of HPM within the framework of fractal calculus is developed, and we investigate its convergence properties and radius of convergence. Several illustrative examples are provided to validate the effectiveness and accuracy of the proposed method. The results demonstrate that HPM offers a powerful and reliable tool for solving fractal differential equations. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.