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Controllability of Fractional Differential Equation of Order α∈(1,2] With Non‐Instantaneous Impulses

The objective of this paper is to establish the sufficient condition for the exact controllability of a control system governed by the fractional differential equation of order α∈(1,2] with non‐instantaneous impulses in a Hilbert space X. The results are obtained using the α‐order cosine family and Banach fixed point theorem. Also, the exact controllability of an integrodifferential problem is studied. Finally, a few examples are given to illustrate the applications of these abstract results.