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.