Controllability of neutral functional differential systems in abstract space

Controllability of Non-densely Defined Neutral Functional Differential Systems in Abstract Space*

“…More precisely, we consider the controllability problem of the following neutral system on a general Banach space X (with the norm · ): The problem of controllability of linear and nonlinear systems represented by ODE in finite dimensional space has been extensively studied. Many authors have extended the controllability concept to infinite dimensional systems in Banach space with unbounded operators (see [1][2][3][4][5][6][7][8][9][10][11] and the references therein). Triggiani [5] established sufficient conditions for controllability of linear and nonlinear systems in Banach space.…”

“…Recently Balachandran and his cooperators have studied the (local) controllability of abstract semilinear functional differential systems (see [9]) and the controllability of abstract integro-differential systems (see [10]). In paper [11] the author has extended the problem to neutral systems with unbounded delay.…”

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

“…Further, B is a bounded linear operator from U to X. Recently, the problems of the controllability of differential systems and integrodifferential systems in Banach spaces were considered by many researchers, see for instance [3,6,13] and the references therein. In the case of the nonlocal condition, the semilinear evolution inclusions has been studied by Benchohra et al [7], Guo et al [17], Li and Xue [19].…”

Regularity for Fractional Order Retarded Neutral Differential Equations in Hilbert Spaces

“…In [4,7,8], the authors have discussed the existence of solutions for mild solutions for the neutral differential systems with state-dependence delay. Most studies about the neutral initial value problems governed by retarded semilinear parabolic equation have been devoted to the control problems.…”