Approximate controllability of fractional order neutral stochastic integro-differential system with nonlocal conditions and infinite delay

Abstract

This paper deals with the approximate controllability of fractional order neutral stochastic integro-differential system with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. With this control function, the sufficient conditions for approximate controllability of the proposed probelm in Hilbert space is established. Further, the results are obtained by using fractional calculus, stochastic analysis techniques, Sadovskii fixed point theorem and similar to the classical linear growth condition and the Lipschitz condition. Finally an example is provided to illustrate the application of the obtained results.