This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, the existence theory of PC-mild solutions is established under the condition of compact resolvent operator. Furthermore, the uniqueness of PC-mild solutions is proved in the case of the noncompact resolvent operator.

中文翻译：

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具有非局部条件的脉冲分数半线性积分微分方程

本文致力于一类具有非局部初始条件的脉冲分数半线性积分微分方程。基于半群理论和一些不动点定理，建立了紧解算子条件下PC-mild解的存在论。此外，在非紧解算子的情况下证明了 PC-mild 解决方案的唯一性。