Existence and uniqueness of mild solutions for fractional impulsive integro-differentialevolution equations of order bm$1<\beta\leq2$with nonlocal 条件

Abstract

This paper investigates the existence and uniqueness ofmild solutions for fractional impulsive integro-differentialevolution equations with nonlocal 条件 of order$1<\\beta\\leq2$. Under two cases where the 解 operator iscompact and noncompact respectively, the existence results of mild solutions areestablished by the (generalized) Darbo fixed point 定理 andSchauder fixed point 定理. Meanwhile, uniqueness of mildsolutions is also given by the (generalized) Banach contractionmapping principle. These results are obtained by the semigroup定理, 解 operator theorems, measures of noncompactness andfixed point 定理. At last, an 例 is presented to illustratethe effectiveness of the main results.