Controllability of impulsive mixed type Volterra–Fredholm stochastic systems with nonlocal conditions

Abstract

SummaryThis paper investigates complete controllability of impulsive mixed type Volterra–Fredholm stochastic systems with nonlocal conditions. Sufficient conditions are established for complete controllability of a class of impulsive stochastic integrodifferential systems with nonlocal conditions. The results are obtained by a fixed point approach on condition that the corresponding linear system is completely controllable. Finally, an example is given to illustrate our results. Copyright © 2014 John Wiley & Sons, Ltd.

The Controllability of Fractional Damped Stochastic Integrodifferential Systems

“…Remark III.8. Several authors in [14,16,19,20,26,29] have studied the existence of solutions and extended the theory of controllability results for integer order systems. Compared to the above, in this paper, we investigate the complete controllability of fractional nonlinear stochastic integrodifferential systems.…”

“…Often these short‐term perturbations are treated as having acted instantaneously or in the form of "impulses." Controllability of impulsive stochastic systems has been investigated in . Liu and Li proposed on the exact controllability of impulsive fractional semilinear functional differential inclusions.…”

“…Controllability results for fractional damped dynamical systems have been discussed in . The sufficient conditions have been obtained in for complete controllability of impulsive mixed type Volterra‐Fredholm stochastic systems with nonlocal conditions, and in existence results for impulsive neutral stochastic functional integro‐differential equations with infinite delay have been reported. However, to the best of the authors' knowledge, the issue of complete controllability of fractional damped stochastic integrodifferential systems in finite dimensional space is a new and open problem in the literature.…”

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

“…During the past few decades, the impulsive systems have attracted the attention of many researchers since impulse effects exist widely in many evolution processes such as economics, mechanics, electronics, telecommunications, and biology, see other works and the references therein.…”