Controllability of a stochastic functional differential equation driven by a fractional Brownian motion

Abstract

Let U, V and W be three Hilbert spaces and let B H be a W-valued fractional Brownian motion with Hurst index H ∈ ( 1 2 , 1). In this paper, we consider the approximate controllability of the Sobolev-type fractional stochastic differential equationwhere c D α is the Caputo fractional derivative of order α ∈ (1 -H, 1), the time history x t : (-∞, 0] → x t (θ ) = x(t + θ ) with t > 0 belonging to the phase space B h , the control

Controllability of higher-order fractional damped stochastic systems with distributed delay

“…Time delay is an inevitable concept on the study of dynamical systems in the real word [16,17,35]. Concerning the controllability of stochastic fractional systems with delays, we point out [9,12,33]. The linear delay differential equations and systems with distributed delays were first studied in [26].…”

Controllability of a Stochastic Neutral Functional Differential Equation Driven by a fBm

“…For the last parts 5 6 [14], we show the existence of solution and approximate controllability of (1.1).…”

“…We refer [12] [13] and references therein for the details of the theory of stochastic calculus for fractional Brownian motion. In [14], authors consider the approximate controllability of a class of Sobolev-type fractional stochastic equation driven by fractional Brownian motion in a Hilbert space.…”