Controllability for Semilinear Fractional Integro-differential Systems with Deviated Argument in Banach Spaces

Finite-Approximate Controllability of ν-Caputo Fractional Systems

“…E α,α −λ n (ν(d) − ν(t)) α (g, e n )e n (η) = 0 on ω × (0, d). According to Proposition 4.2 in [38], this implies that g = 0 on Ω × (0, d), which is equivalent to the approximate controllability of the linear system associated with (11). Therefore, with the additional assumption of the uniform boundedness of F, the system (11) is finite-approximately controllable over the interval [0, d].…”

“…Later, this method is successfully applied to fractional semilinear evolution systems in the work of Sakthivel et al in [7]. Thereafter, several researchers, Bora et al [8], Kavitha et al [9], Haq et al [10], Aimene [11], Bedi [12], Matar [13], Ge et al [14], Grudzka et al [15], Ke et al [16], Kumar et al [17,18], Liu et al [19], Sakthivel et al [20], Wang et al [21], Yan [22], Yang et al [23], Rykaczewski [24] have used different methods to study approximate controllability for several fractional differential and integro-differential systems. • Thereafter, several researchers, Vijayakumar et al [25], Ding et al [26], Bose et al [27] studied the approximate reachability for different kind of ν-fractional systems.…”

Finite-Approximate Controllability of Riemann–Liouville Fractional Evolution Systems via Resolvent-Like Operators

“…Later, this method was adapted to study the approximate controllability of fractional semilinear evolution systems by Sakthivel et al [23]. Thereafter, several researchers, Bora and Roy [24], Dhayal and Malik [25], Kavitha et al [26], Haq and Sukavanam [27], Aimene [28],…”