The Solvability Of A Class Of Impulsive Fuzzy Differential Equations On Time Scales

In recent years,many scholars have studied the fuzzy differential equations on time scale.For example,in the article?Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales[J].Abstract&Applied Analysis,2014,2014(1):1-19?,the author considers the nonlinear impulsive set-valued dynamic equation,which is impul-sive set-valued dynamic equation on time scale,and it obtained some new criteria for the existence and stability of the solution of that equation.At the same time,it is pointed out that the results can be used to study the related problems of fuzzy differential equa-tion.Inspired by the above researches.in this thesis,author first defines the generalized derivative of fuzzy function,then use the exponential dichotomy of the set-valued func-tion,gives the corresponding concept of the fuzzy function,introduces the fixed point theory,and discusses the existence and uniqueness of the solution of linear impulsive fuzzy differential equation on time scale and the existence of the solution of nonlinear impulsive fuzzy differential equation on time scale,respectively.The thesis is divided into four chapters,and the specific arrangements are as follows:The first chapter is the introduction,which makes a brief review of fuzzy mathemat-ics from the perspective of research background and current research status.In particular,it makes a necessary analysis of the research status of fuzzy differential equation at home and abroad,and makes a detailed introduction to the fuzzy differential equation on the time scale.The second chapter is the preliminary knowledge,which mainly gives some related definitions,theorems and lemmas,these are references to existing research results.How-ever,in the third chapter's proof,especially in explaining the definition and the nature of the exponential dichotomy,this preliminary knowledge is very useful.The third chapter is the main result.When discussing the existence and uniqueness of solution of linear impulsive fuzzy differential equation,we first prove the existence and boundedness of solutions by using lemma 2.8,lemma 2.9 and exponential dichotomy,and then prove the uniqueness of solution by using exponential dichotomy.Based on this,the fixed point theory is used to prove the existence of the solution of the nonlinear impulsive fuzzy differential equation.Finally,the main work of this thesis is summarized,and the future work and possible future research direction are prospected.