In this paper, we consider a class of fractional semilinear integrodifferential equations with noninstantaneous impulses and delay. By the semigroup theory and fixed point theorems, we establish various theorems for the existence of mild solutions for the problem. An example involving partial differential equations with noninstantaneous impulses is given to show the application of our main results.

中文翻译：

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具有非瞬时脉冲和时滞的分数阶半线性积分微分方程的存在性定理

在本文中，我们考虑一类具有非瞬时脉冲和时滞的分数阶半线性积分微分方程。通过半群理论和不动点定理，我们建立了针对该问题的温和解的各种定理。给出了一个包含具有非瞬时脉冲的偏微分方程的例子，以说明我们的主要结果的应用。