Approximate Controllability of Fractional Order Semilinear Delay Systems

Approximate Controllability Results for Fractional Semilinear Integro-Differential Inclusions in Hilbert Spaces

“…In [35], Mahmudov proved the approximate controllability of fractional evolution equations by using of the theory of fractional calculus, semigroup theory and the Schauder's fixed point theorem. In [46], Sukavanam discussed the approximate controllability of a delayed semilinear control system with growing nonlinear term by using Schauder's fixed point theorem. Very recently, in [44] Sakthivel et al studied the approximate controllability of fractional nonlinear differential inclusions with initial and nonlocal conditions by using Bohnenblust-Karlin's fixed point theorem.…”

Regularity for Fractional Order Retarded Neutral Differential Equations in Hilbert Spaces

“…Most studies about the neutral initial value problems governed by retarded semilinear parabolic equation have been devoted to the control problems. As for the retarded differential equations, Jeong et al [12,13], Sukavanam et al [22], and Wang [25], have discussed the regularity of solutions and controllability of the semilinear retarded systems, and see [12,13,22,25] and references therein for the linear retarded systems.…”

“…In addition, Sukavanam et al [21] studied approximate controllability of fractional order semilinear delay systems.…”

Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps

“…However, if the compactness condition holds on the bounded operator that maps the control function on the generated C 0 -semigroup, then the controllability operator is also compact and its inverse does not exist if the state space is infinite-dimensional (see [28]). Sukavanam et al [25] have proved some sufficient conditions for the approximate controllability of fractional order system in which the nonlinear term depends on both state and control variables. Balasubramaniam et al [1] discussed the approximate controllability of impulsive fractional integro-differential systems with nonlocal conditions in Hilbert space by using Darbo-Sadovskii's fixed-point theorem.…”