Controllability of Volterra–Fredholm type systems in Banach spaces

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

“…Introducing the concept of PC-mild solutions and using the piecewise continuous control functions and uniformly continuous semigroup, we obtained the controllability results for the corresponding fractional impulsive integrodifferential system. 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.…”

Nonlocal cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities

“…It should be clarified that conditions (A) and (B), assumed in several papers in order to obtain the controllability (see for instance the recent [9], [17]), implicitly imply that the Banach space E has finite dimension, as proved by Hernández and O'Regan in [12].…”

Exact Controllability for Hilfer Fractional Differential Inclusions Involving Nonlocal Initial Conditions

“…Controllability is one of the fundamental concepts in mathematical control theory, it means that it is possible to steer a dynamical system from an arbitrary initial state to arbitrary final state using the set of admissible controls. Recently, the controllability conditions for various linear and nonlinear integer or fractional order systems have been considered in many papers by using different methods [20][21][22][23][24][25][26][27][28][29][30][31][32][33] and the references. There have also been some results [20-24, 32, 33] about the investigations of the exact controllability of systems represented by nonlinear evolution equations in infinite dimensional space.…”

“…There have also been some results [20-24, 32, 33] about the investigations of the exact controllability of systems represented by nonlinear evolution equations in infinite dimensional space. But when the semigroup or the control action operator B is compact, then the controllability operator is also compact and the applications of exact controllability results is just restricted to the finite dimensional space [20]. Therefore, we investigate the exact controllability of the fractional evolution systems only involving noncompact semigroups.…”