In this paper, we concern on the periodic boundary value problem for a class of semilinear impulsive fractional evolution equations in an ordered Banach space E. First, we establish the existence results of mild solutions for the associated linear periodic boundary value problem. Next, we obtain the existence results of mild solutions by using the monotone iterative technique with L-quasi-upper and lower solutions, the results are new and extend some previously known results. Finally, two examples are also given to illustrate the main results.

中文翻译：

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具有周期边界条件的脉冲分数阶演化方程的温和解的存在性

在本文中，我们关注有序Banach空间E中一类半线性脉冲分数阶演化方程的周期边值问题。首先，我们建立了相关线性周期边值问题的温和解的存在性结果。接下来，我们通过使用具有L-拟上和下解的单调迭代技术获得温和解的存在结果，该结果是新的并扩展了一些先前已知的结果。最后，还给出了两个例子来说明主要结果。