An Analytical Study for the System of Nonlinear Fuzzy Differential Equations with a Consequent Application
Payal Singh
1
(
Department of Applied Sciences and Humanities, Parul Institute of Engineering & Technology, Parul University, Vadodara 391760, Gujarat, India.
)
Kamal Hossain Gazi
2
(
Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia 741249, West Bengal, India.
)
Mohammed Rabih
3
(
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia.
)
K. Rangarajan
4
(
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai-602105, Tamil Nadu, India.
)
Sankar Prasad Mondal
5
(
Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia 741249, West Bengal, India.
)
الکلمات المفتاحية: Fuzzy nonlinear differential equations, Fuzzy solution, Fuzzy sequence, Fixed point theorem, Numerical simulation.,
ملخص المقالة :
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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