Investigating Mild Solutions for Noninstantaneous Impulsive Caputo Fractional Integro‐Differential Equations

In this paper, the existence of mild solutions for a class of noninstantaneous impulsive Caputo fractional integro‐differential equations subject to nonlocal conditions in Banach spaces is investigated. The problem is formulated in a general infinite‐dimensional setting so that systems involving memory effects and impulses acting over finite intervals can be described. The analysis is carried out through the combined application of Mönch′s fixed‐point theorem, Grimmer′s resolvent operator framework, and measures of noncompactness, by which the lack of compactness is effectively handled and suitable existence conditions are established. The obtained results are regarded as an extension of several existing theories since more general assumptions and dynamical behaviors are accommodated. Moreover, an explicit example is provided to illustrate the applicability of the theoretical results and to demonstrate how the proposed assumptions can be verified in concrete cases.