Title: Initial value solution of differential equations based on fuzzy system theory

Authors: Xiaohui Zhang; Weiqiang Niu

Addresses: School of Mathematics and Statistic, Zhengzhou Normal University, Zhengzhou 450044, China ' School of Mathematics and Statistic, Zhengzhou Normal University, Zhengzhou 450044, China

Abstract: The research addresses the initial value problem of fuzzy differential equations, emphasising solution stability. By utilising fuzzy system theory and differential envelope theory, a relationship between differential envelope solutions and fuzzy differential equation solutions is established, and the stability of these solutions is analysed. The method is effectively applied to the stability analysis of uncertain dynamic systems, revealing that the relative error of the analytic solution y is under 0.2%, while the standard error of solution z is within 0.3%. The displacement of the midpoint of an elastic vertical plate and the radiation wave height for l/d = 4 show sensitivity to the stiffness coefficient and pulse amplitude, positively affecting vibration response and radiation height. Additionally, the decay rate for fixed boundary conditions is significantly faster than for the other conditions. The proposed method demonstrates high stability in solving the initial value problem of fuzzy differential equations.

Keywords: fuzzy system theory; differential equation; initial value problem; stability; uncertain dynamical system.

DOI: 10.1504/IJDSDE.2024.145816

International Journal of Dynamical Systems and Differential Equations, 2024 Vol.13 No.6, pp.533 - 548

Received: 04 Sep 2024
Accepted: 24 Oct 2024
Published online: 25 Apr 2025 *

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