A comprehensive literature review of fuzzy differential equations with applications

Abstract

Physical dynamical systems can be described through mathematical models using the theory of differential equations. Many different types of uncertain healing occur in the real-world. Fuzzy logic is an effective mathematical tool for defining the sense of non-random uncertainty. Since fuzzy arithmetic differs from its counterparts, it would be more reliable if we use the differential equation to construct models involving uncertain decision parameters. In this paper, we attempt a detailed review of the existing literature related to the theory and application of fuzzy differential equations. The scientific review of this paper includes surveys of the Literature involving different definitions of fuzzy derivation. Distinguished solution approaches and applications of fuzzy differential equations in the fields of science, technology, and management are discussed in this paper. We also provide hints regarding future research challenges and scopes with the theory of fuzzy differential equations. This paper may be impactful documentation of the history of differential equations linking the past, present and future of the concerned research topic.

Keywords

• fuzzy differential equations
• fuzzy derivatives
• fuzzy sets
• fuzzy numbers