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

Document Type : Research Article

Authors

1 University of applied sciences and technology of center Mahan Hedayat, Mahan Hedayat, Iran

2 ‎Department of Mathematics‎, ‎Science and Reseek Branch‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran

3 Department of Mathematics‎, ‎WT.C‎, ‎Islamic Azad University‎, ‎Tehran‎, ‎Iran

4 Department of Mathematics Qazvin Branch, Islamic Azad University, Qazvin, Iran

10.22128/ansne.2025.3017.1145

Abstract

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.

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References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 2
September 2025
Pages 184-192

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History

  • Receive Date: 13 August 2025
  • Revise Date: 21 August 2025
  • Accept Date: 09 September 2025
  • Publish Date: 24 September 2025

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