Solvability For A Class Of Nonlinear Fuzzy Volterra Integro-differential Equations

Fuzzy mathematics is a branch of mathematics to study and deal with fuzzy phenomena.In the past 50 years,fuzzy theory and technology have developed rapidly,and scholars at home and abroad have done a lot of effective work in this field.Among them,the research on fuzzy differential equation and fuzzy integral equation is one of the hot topics in the field of fuzzy mathematics.In this paper,we mainly discuss the analytical the existence and uniqueness of solutions for nonlinear fuzzy Volterra integro-differential equations,By extending the characteristic theorem of Bede,we obtain the analytical expression of the solutions to the nonlinear Fuzzy Volterra integro-differential equations.The full text is divided into four chapters:Chapter 1 is the introduction.We introduce fuzzy mathematics from the research background,research status and so on.In this process,we introduce fuzzy differential equation,fuzzy integral equation and Fuzzy Volterra integro-differential equations in detail.Chapter 2 is preliminaries.In this chapter,some basic concepts,theorems and lemmas related to this paper are given.These will play important roles in the following chapters.Chapter 3 is the main results.In this chapter,we mainly dicuss the existence and uniqueness of solutions of nonlinear fuzzy Volterra intgro-differential equations and characteristic theorem.We prove the existence and uniqueness of the solution of nonlinear fuzzy Volterra intgro-differential equations by using the contraction theorem,and transform the equation into a system of Integro-differential equations by using the characteristic theorem,so as to find the solution of the equations.Chapter 4 is the summary and prospect.In this chapter,we summarize the full text,discuss about some shortcomings and put forward some feasible directions for the future research.