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
In this paper, we consider a class of Sobolev-type fractional neutral stochastic differential equations driven by fractional Brownian motion with infinite delay in a Hilbert space. When 1 H α > − , by the technique of Sadovskii's fixed point theorem, stochastic calculus and the methods adopted directly from deterministic control problems, we study the approximate controllability of the stochastic system.
In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.