Stability Study Of Fuzzy Differential Equations Initial Value Problems

In the nature, there is a kind of special dynamical system which is uncertain or incomplete. This kind of uncertain dynamical systems can be described as fuzzy differential equations in a good way, so many people are interested in this kind of uncertain dynamical systems and many mathematicians are interested in studying fuzzy differential equations theory.The study of fuzzy differential equations theory is mainly concentrated on all kinds of rich properties of the solutions, which includes existence problems, uniqueness problems, initial value problems, boundary value problems, periodicity problems, stability problems and other problems like attractors, boundary, bifurcation and so on. These rich properties are good at describing and explicating the long-term behavior of the solutions of fuzzy differential equations.Now there are mainly three kinds of methods to study fuzzy differential equations theory. The first method is to define Hukuhara derivative of a fuzzy-number-valued function, which is called H-derivative in short, to study fuzzy differential equations. The second method is to use generalized differentiabilities to study fuzzy differential equations, which contains strongly generalized differentiabilities and weakly generalized differentiabilities. The third method is to use differential inclusions theory to study fuzzy differential equations indirectly.This paper is to study the stability of fuzzy differential equations initial value problems with the help of differential inclusions. The first step is to study the stability of differential inclusions problems. The second step is to study the stability of fuzzy differential equations with the help of the one-one relationships between the solutions of differential inclusions problems and the solutions of fuzzy differential equations.The purpose of this paper is to discuss the definition of stability of fuzzy differential equations, and make it reasonable in any ways.