Existence And Uniqueness Of The Solutions For Complex Uncertain Differential Equations

A lot of uncertain phenomena exist in nature.And there are more and more uncertaint events in our life along with the development of times and the advancement of technologies.As a result,there are more and more matters that can not be settled by probability theory and fuzzy theory.In order to solve these questions better,uncertainty theory were presented.Uncertainty theory is a new axiomatic system for dealing with subjective uncertainty of people.Under the framework of uncertainty theory,the paper researches strong comonotonic uncertain process and studied some properties of integral by using strong comonotonic uncertain process.Then we study complex uncertain process and complex uncertain distribution,obtain some properties of complex uncertain process,uncertain integral and complex uncertain integral.At last,the solution methods of complex uncertain differential equation are discussed.Furthermore,the existence and uniqueness of solutions of complex uncertain differential equations are derived.The main contents of this paper is as follows:1.we deduce some theorems about mathematical operations such as addition,and scalar multiplication of strong comonotonic uncertain process and prove some theorems about uncertain integral based on strong comonotonic uncertain process including nonnegativity,monotonicity and several inequalities.2.we propose the concept of complex uncertain distribution of complex uncertain process and prove a sufficient and necessary condition of it.And then we study the independence,expected value and variance of complex uncertain process,the existence of uncertain integral and complex uncertain integral.Next,we discuss some basic properties of other uncertain integral.3.we reseach the solutions of complex uncertain differential equations,and prove the existence and uniqueness theorems for complex uncertain differential equations.