The Existence And Uniqueness Of Solution To First-order Fuzzy Functional Differential Equations

The theory of fuzzy set is the further development of classic set, which hold the view that elements always belong to one or several sets in a degree. The theory of fuzzy set was proposed by Zadeh in 1965. So the fuzzy math was created. The theory of fuzzy with a wide range of applications set is the spread of classical set. The element belongs to a set or belongs to some sets with some extent. In recent years, functional differential equations has played an important role in an increasing number of system models in biology, engineering, physics and other sciences with the gradual maturity of related theories and wide application. There exists extensive research and achievements for the learners on the functional differential equations and their applications, which is still a focus for study in international academic circles at present.The paper consists there parts. The first part deals with the approximate solutions and its uniqueness for existence of the first-order fuzzy functional integral equations. The second part deals with the uniqueness for existence of the first-order fuzzy functional differential equations. The third part deals with the application of the first-order fuzzy functional differential equations. Main aspects can be summarized as follows:1) we discussed the properties of the sequence of fuzzy successive approximations and introduced several properties of fuzzy sequence about equicontinuous and converges uniformly,we study the existence of the first-order fuzzy functional integral equations using the method of successive approximations and introduced some sufficient conditions of the existence of the first-order fuzzy functional differential equations2) we study the local uniqueness and existence of the first-order fuzzy functional differential equations and introduced some sufficient conditions of the local existence and uniqueness.3) Prove the existence and uniqueness of solution of the first-order fuzzy functional differential equations and introduced some sufficient conditions of the global existence and uniqueness.4) Two examples of the application fuzzy functional differential equations,one is time-delay Malthusian model the other is Ehrlich ascities tumor Finally.