An Analytical Study for the System of Nonlinear Fuzzy Differential Equations with a Consequent Application

Payal Singh ¹ ( )
Kamal Hossain Gazi ² ( )
Mohammed Rabih ³ ( )
K. Rangarajan ⁴ ( )
Sankar Prasad Mondal ⁵ ( )

Submited date : 2025-05-22 Accepted date : 2025-08-17

Keywords: Fuzzy nonlinear differential equations, Fuzzy solution, Fuzzy sequence, Fixed point theorem, Numerical simulation.,

Abstract :

Realistic scenarios typically involve several interacting dependent variables, leading to nonlinearity in mathematical models. Nonlinear differential equations are a crucial mathematical phenomenon for describing real-world problems. On the other hand, fuzzy set theory is a valuable tool for modelling the uncertainty present in a system. So, nonlinear mathematical models under uncertainty need an explanatory study on a system of nonlinear fuzzy differential equations. In this paper, we analyse nonlinear fuzzy differential equations with possible applications. This paper advances the existing literature by introducing a definition of a fuzzy sequence and developing the existence and uniqueness theory for fuzzy solutions of nonlinear differential equations using the fixed-point theorem. The component-wise analysis of a fuzzy nonlinear system has been conducted. Furthermore, the analysed theory precedes an aptly fitted application of a fuzzy nonlinear dynamical system using a numerical scheme.

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