The Research Of The Initial Value Problems Of Some Fuzzy Differential Equations

This paper will be divided into five chapters. The first three chapters is the foundationof this paper. In this part, we firstly give the concept of fuzzy number and fuzzy numberspace and two special kinds of fuzzy numbers-continuous fuzzy number. Secondly webuild new parameter representation and description of the continuous fuzzy number. Fuzzynumber valued functions also is our object of research, so thirdly we give the calculus andthe new calculus theory of fuzzy number valued functions on the basis of new parametricrepresentation of fuzzy number. Research of initial value problems have to be completedon the basis of the above content.Nieto J had given a Peano theorem of fuzzy differential equations, and which had bewidely applied. In recent years, the Choudary A D R pointed out the lack of this theorem,and held a counter-example. At the fifth chapter paper, we firstly build some theory offuzzy numerical function on the continuous fuzzy number space, then we continue to studythe peano theorem,combining the new parameters of continuous fuzzy numbers on thebasis of the above basic theory. We will give new conditions to fix its shortage, Finally weget some theory of fuzzy initial value problems.At the last chapter we define the system of fuzzy differential equations and study thesystem on the condition of generalized fuzzy differentiation. Finally we will get the newmethod of solving fuzzy differential equation, transforming the system of FDEs to asystem of real-valued differential equations and give a example.