Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 9 2 2025 09 24 Application of the Homotopy Perturbation Method for Approximating Solutions to Fuzzy Initial Value Problems under Generalized Differentiable 184 192 1907 10.22128/ansne.2025.3017.1145 EN Samira Siahmansouri University of applied sciences and technology of center Mahan Hedayat, Mahan Hedayat, Iran 0000-0003-1750-6393 Esmaeil Yousefi ‎Department of Mathematics‎, ‎Science and Reseek Branch‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran 0000-0002-0977-7030 Mohammad Gholamian Department of Mathematics‎, ‎WT.C‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran 0000-0002-0779-7695 Samaneh Neyshabouri Department of Mathematics Qazvin Branch, Islamic Azad University, Qazvin, Iran 0000-0003-1515-0653 Journal Article 2025 08 13 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. https://ansne.du.ac.ir/article_1907_647b8b4b31d781eff3d42166e2f287f3.pdf