Existence and uniqueness of mild solution for initial value problem of a class of fuzzy evolution equations with delay

In this paper, we consider a class of fuzzy delay evolution equations under generalized differentiability. By using the operator semigroup theory, the upper and lower solutions and the monotoneiterative technique, the existence and uniqueness of mild solutions for the initial value problem of fuzzydelay evolution equations are obtained. The continuous dependence of two kinds of mild solutions onthe initial value is also proved. In particular, the first innovation of this paper is to introduce the delayterm into the fuzzy evolution equation, and the second innovation is that when discussing the continuousdependence of the solution on the initial value, it completely eliminates the restriction of the nonlinearfunction on the Lipschitz condition coefficients and optimizes the conditions for the existence of the solutions, which is relatively rare. Corresponding examples are added at the end of the article to make theconclusion better applied to practice.

کلیدواژه ها:

Fuzzy delay evolution equations ، monotone iterative technique ، fuzzy strongly continuous semigroup ، fuzzy mild solution ، Existence and uniqueness