半线性分数次发展方程的非局部Cauchy问题

THE CAUCHY PROBLEM OF SIMILINEAR FRACTIONAL EVOLUTION EQUATION WITH NONLOCAL CONDITION

针对一种定义在Banach空间上的带有非局部条件的半线性分数次发展方程的Cauchy问题,利用krasnoselkii不动点定理,得到了mild解的存在性定理。最后,应用我们给出的定理证明了一类微分方程mild解的存在性。

We discuss in this paper the existence and uniqueness of mild solution to the Cau-chy problem for the semilinear fractional evolution equations with nonlocal conditions in a Banach spaces.New results are given.Finally,we give an example to illustrate our main result.