Solving fuzzy Riccati differential equations with Trapezoidal fuzzy functions by Homotopy perturbation method

Authors

DOI:

https://doi.org/10.19139/soic-2310-5070-3789

Keywords:

Trapezoidal fuzzy number (TFN), Fuzzy Quadratic Riccati differential equation (FQRDE), Homotopy perturbation method (HPM), He's polynomials (HePs), Accelerated Adomian polynomials (AAPs), Stability analysis with trapezoidal fuzzy numbers

Abstract

This study innovatively combines the homotopy perturbation method (HPM) with trapezoidal fuzzy functions to solve nonlinear Riccati differential equations under uncertainty. By decomposing fuzzy equations into α-cut systems and solving coupled crisp problems via HPM, the approach preserves trapezoidal fuzzy structures while ensuring computational efficiency and precision, The stability behavior of the fuzzy Riccati differential equation was also studied, and good and highly efficient results were obtained in convergence of α values. This convergence was proven theoretically and numerically. Numerical results validate its rapid convergence and accuracy, as for the numerical results, He's polynomials and the accelerated Adomian polynomials were used. The framework extends HPM's applicability to complex uncertainty modeling, offering a robust tool for control theory and engineering systems with trapezoidal fuzzy parameters.  

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Published

2026-07-31

How to Cite

Younis, M. T., Yassin, Z. T., & Al-Hayani, W. M. (2026). Solving fuzzy Riccati differential equations with Trapezoidal fuzzy functions by Homotopy perturbation method. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-3789

Issue

Online First

Section

Research Articles

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Copyright (c) 2026 Mahasin Thabet Younis, Zena Talal Yassin, Waleed Mohammed Al-Hayani

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