Approximate controllability of semilinear retarded stochastic differential system with non-instantaneous impulses: Fredholm theory approach

This article deals with the approximate controllability of semilinear retarded integrodifferential equations with non-instantaneous impulses governed by Poisson jumps in Hilbert space. The existence of a mild solution is established by using stochastic calculus and a suitable fixed point technique. The approximate controllability of the proposed non-linear stochastic differential system is obtained by employing the theory of interpolation spaces and Fredholm theory. Finally, applications to the stochastic heat equation and retarded type stochastic Benjamin-Bona-Mahony equation are provided to illustrate the developed theoretical results.