Controllability analysis for coupled integrodifferential equations under resolvent and history-dependent operators

In this article, we advance the state of controllability theory by establishing pioneering conditions for nonlocal integrodifferential equations operating in vector Banach spaces. The primary contribution of this work is the simultaneous integration of history-dependent operators and resolvent operators framed within the spatial structure of the α-norm. Moving beyond standard assumptions, we employ fractional calculus paired with generalized measures of noncompactness to bypass conventional compactness requirements for condensing operators. This allows us to significantly broaden previous controllability results under the baseline assumption of linear system controllability, culminating in a rigorous theoretical framework that we validate through an illustrative concrete example.