PC-Mild Solutions to Sobolev-Type Fractional Differential Equations with Non-instantaneous Impulses

摘要

In this paper, we study the existence and uniqueness of piecewise-continuous (in brief, PC)-mild solutions for Sobolev-type fractional impulsive differential equations (in brief, STFIDEs) with state-dependent delay by virtue of Kuratowski measure of noncompactness in a Banach space. We establish a general framework to find PC-mild solutions for STFIDEs with compact and noncompact semigroups, which will provide an effective way to deal with such problems. Finally, an application is given to illustrate that our results are valuable.