New discussion on the existence and controllability of fractional evolution inclusion of order 1 < r < 2 without compactness

Abstract

In this article, we investigate the existence and controllability results for fractional evolution inclusions in Banach spaces. By eliminating compactness hypotheses on the semigroup produced by the linear component and any requirements on the multivalued nonlinearity defined in terms of measures of noncompactness, we apply a new method to arrive at the existence of mild solutions and controllability results. In fact, to satisfy the existence and controllability requirements, we propose a fixed‐point strategy for weakly sequentially closed maps. Finally, a concrete example is provided to highlight our theoretical findings.