Application of the Homotopy Perturbation Method for Approximating Solutions to Fuzzy Initial Value Problems under Generalized Differentiable

In this paper, ‎the Homotopy Perturbation Method (HPM) is employed to obtain approximate semi-analytical solutions for Fuzzy Initial Value Problems (FIVPs) within the framework of generalized differentiable. ‎The original FIVP is reformulated as a pair of parameterized ordinary differential equations, ‎which are then solved iteratively using HPM‎. ‎Numerical results show that the approximate solutions converge rapidly to the exact fuzzy solutions, ‎achieving high accuracy even with a limited number of perturbation terms. ‎These findings underscore HPMs effectiveness as a simple yet powerful technique for addressing fuzzy differential equations. ‎Moreover, ‎the methods flexibility indicates its potential for solving higher-order and more complex fuzzy differential systems. ‎Recent studies including the application of HPM to fuzzy impulsive fractional differential equations under generalized Hukuhara differentiable, ‎as well as hybrid and transform-based extensions such as the Elzaki Transform Homotopy Perturbation Method (ETHPM) further highlight the evolving scope and versatility of HPM in fuzzy problem-solving contexts.

کلیدواژه ها:

Homotopy Perturbation Method (HPM)‎ ، ‎Fuzzy Initial Value Problems (FIVPs)‎ ، ‎Generalized Differentiability‎ ، ‎Semi-analytical Approximation