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Herein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order α∈(1,2), where the linear part is a strongly continuous cosine family without compactness. We did not assume any compactness conditions on either the semi-group, the multi-valued function, or the inverse of the controllability operator, which is different from the previous literature.

Controllability of Semilinear Multi-Valued Differential Inclusions with Non-Instantaneous Impulses of Order α ∈ (1,2) without Compactness