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

Abstract

Abstract 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.