“…On the other hand, in recent years, much attention has been paid to establishing sufficient conditions for the controllability of linear fractional dynamical systems of order 0 < α < 1 by several authors; see a recent monograph [1,2,4,5,8,22,23] and various papers [2,6]. However, there is no work that reported on the problem of controllability of nonlinear fractional dynamical system of order 1 < α < 2, to the best of our knowledge, up until now the controllability for a class of impulsive fractional integro-differential evolution equation with fractional derivative of order α ∈ (1, 2] has not been investigated in the literature.…”