Approximate controllability of impulsive partial neutral stochastic functional integro-differential inclusions with infinite delay

Zuomao Yan,Fangxia Lu

doi:10.1186/s13662-015-0368-z

Zuomao Yan, Fangxia Lu

Open Access

https://doi.org/10.1186/s13662-015-0368-z

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Abstract

In this paper, the approximate controllability of partial neutral stochastic functional integro-differential inclusions with infinite delay and impulsive effects in Hilbert spaces is considered. By using Holder’s inequality, stochastic analysis and fixed point strategy with the properties of analytic resolvent operator, a new set of sufficient conditions is formulated, which guarantees the approximate controllability of the nonlinear impulsive stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is given to illustrate our results.

Highlights

The study of controllability plays an important role in the control theory and engineering [ ]
In this paper we study the approximate controllability of a class of impulsive partial neutral stochastic functional integro-differential inclusions with infinite delay in Hilbert spaces of the form t d x(t) – G(t, xt) ∈ A x(t) + h(t – s)x(s) ds dt + Bu(t) dt + F(t, xt) dw(t)
To the best of our knowledge, there are no relevant reports on the approximate controllability of impulsive partial stochastic functional integrodifferential inclusions with infinite delay and resolvent operator in the current paper, which is expressed in the form ( . )-( . )

Summary

Introduction

The study of controllability plays an important role in the control theory and engineering [ ]. The papers [ – ] studied the existence of mild solutions for some impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. In this paper we study the approximate controllability of a class of impulsive partial neutral stochastic functional integro-differential inclusions with infinite delay in Hilbert spaces of the form t d x(t) – G(t, xt) ∈ A x(t) + h(t – s)x(s) ds dt + Bu(t) dt + F(t, xt) dw(t),. To the best of our knowledge, there are no relevant reports on the approximate controllability of impulsive partial stochastic functional integrodifferential inclusions with infinite delay and resolvent operator in the current paper, which is expressed in the form

Preliminaries

Conclusion