Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space

Abstract

In this paper, sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the Leray-Schauder nonlinear alternative. An example is provided to illustrate the theory.

Approximate Controllability of Impulsive Stochastic Evolution Equations

“…The technique used here can be extended to investigate the approximate controllability of nonlinear impulsive stochastic functional di¤er-ential equations with unbounded delay by suitably introducing the phase space defined in [3,4].…”

Existence and Dependence Results for Semilinear Functional Stochastic Differential Equations with Infinite Delay in a Hilbert Space

“…In the case of stochastic equations with finite delay, the literature is rich, see the survey of Ivanov-Kazmerchuk-Swishchuk [13]. Stochastic equations with infinite delay are more complicated (see [4,15,20,21,23]), the most general approach, initiated by Hale and Kato [10,16], consists of taking the initial condition in an abstract seminormed space phase space. This kind of space is defined axiomatically, of course, a concrete choice of this space depends on the particular problem under investigation.…”

Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function

“…Numerous works are committed to the study of existence, controllability and stability properties http://dx.doi.org/10.1016/j.amc.2015.01.035 0096-3003/Ó 2015 Elsevier Inc. All rights reserved. of differential inclusions [5][6][7]29,30]. El-Sayed and Ibrahim [12] initiated the study of FDI and consequently various results have been developed, see [1,21,[37][38][39][40][41].…”