In this paper, we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo’s fractional derivatives. By using the measure of noncompactness, β-resolvent family, fixed point theorems and Banach contraction mapping principle, we improve and generalizes some related results on this topic. At last, we give an example to illustrate the application of the main results of this paper.

中文翻译：

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一类带时滞的分数阶非自治发展方程的温和解的存在性

在本文中，我们考虑了一类带时滞的分数阶非自治演化方程和Caputo分数阶导数的温和解的存在性和唯一性。通过使用非紧致性，β-溶剂族，定点定理和Banach压缩映射原理的度量，我们改进并归纳了与此主题相关的一些结果。最后，我们以一个例子来说明本文主要结果的应用。