A Class Of Fuzzy Derivatives And Fuzzy Differential Equations On Time Scales

In this thesis,we use the interactive fuzzy process of joint probability distribution,completely correlated and linear correlated in real number field and the fuzzy derivative of linear correlated as tools to get the interactive fuzzy process of joint probability distri-bution,completely correlated and linear correlated on time scales and the fuzzy derivative on time scales.In order to get our results,we first introduce the interactive fuzzy process of joint probability distribution,completely correlated and linear correlated in real num-ber field,and then apply these concepts and theorems to time scales.In the literature,we mainly discuss Hukuhara derivatives,extended Hukuhara derivatives and the existence of their linear and nonlinear solutions in the real number field,and then extend them to the order of n.In recent years,there are many discussions on Hukuhara derivative,extended Hukuhara derivative and the existence of their linear and nonlinear solutions.However,the discussion of linear correlated derivative in real number field is relatively less,and the discussion of linear correlation derivative on time scale is also less,which is worth further discussion.In this thesis,we mainly study the interactive fuzzy process and the fuzzy deriva-tive of linear correlated on time scales,and discuss the existence of solutions of linear and nonlinear fuzzy differential equation on time scales.The thesis is divided into four chapters:The first chapter is the introduction.In this chapter,we introduce the research back-ground of fuzzy differential equation on time scales,the research status and development trend at home and abroad in recent decades,and finally give the main content of this thesis.The second chapter is preliminaries.We introduce the concepts of fuzzy number,joint probability distribution,completely correlated and linear correlated,define differ-ence and sum of a pair of fuzzy numbers,as well as,we give the fuzzy substitution process,fuzzy derivative and integral of fuzzy function on time scales.The third chapter is a class of fuzzy derivatives on time scales.This chapter mainly discusses the linear correlated fuzzy derivative and its properties,linear correlation inte-gral and its properties.In the fourth chapter,we discuss the existence of several classes of fuzzy differential equations on time scales.This chapter is divided into two parts.The first part mainly discusses the solution of the linear fuzzy differential equation(?)where,t?[t0,T](?)T,?(t)T?(0,?),y0?Tf.Moreover,we are concerned with the following(?) where,t?[t0,T](?)T,?(t):T?(0,?),Y0,b(t)?Tf.In the second part,the solutions of nonlinear fuzzy differential equations are dis-cussed(?) where,t?[t0,T](?)T,s?T,y0?Tf,F:T× Tf?Tf is a continuous fuzzy mapping,K:T ×T × Tf?Tf is a continuous fuzzy mapping.We discuss the existence of solutions when the derivative is linear correlated derivative,and give its proof.We also give the condition to guarantee the equation has an unique solution.The fifth Chapter is the summary and prospect of this thesis.To wit,we summarize the whole thesis and put forward the future research direction.