Comments on Some Recent Results on Controllability of Abstract Differential Problems

Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions

“…Assuming that the semigroup is compact and utilizing some additional conditions, Hernández and O'Regan [30] showed that some known results on exact controllability (see the references cited therein) are valid if and only if the Banach space is finite dimensional. Recently, Hernández et al [31] pointed out that some recent results on exact controllability of abstract differential systems with an unbounded linear operator dominated by a sectorial operator were not applicable. Contrary to those results, we do not need in our results conflicting conditions, which, in a certain sense, is a significant improvement compared to the results in the cited papers.…”

On The Exact Controllability of Impulsive Fractional Semilinear Functional Differential Inclusions

“…, for more details, see [1,9,13,15,23,27]. Unfortunately, this assumption is rather difficult to verify directly in practice.…”

“…Generally speaking, the significance of the controllability lies in the fact that it can steer a dynamic control system from an arbitrary initial state to arbitrary final state using the set of admissible controls. Recently, most of the exact controllability results have been generalized to the infinite dimensional context by the assumption that the linear operator , associated with the semigroup T ( t )( t > 0), has a bounded inverse operator with values in , for more details, see . Unfortunately, this assumption is rather difficult to verify directly in practice.…”