Abstract In this paper, we focus on investigating the existence of mild solutions and the stability analysis of fractional evolution equations involving finite time delay and maxima. Our approach relies on tools such as the measure of non-compactness, the concept of p {p} -set contractions, and the Banach contraction principle. Additionally, we employ a generalized form of Gronwall’s inequality to examine various types of stability. To demonstrate the applicability of our theoretical findings, a concrete example is provided.
Abdeldjebbar et al. (Fri,) studied this question.