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

Abstract

Abstract 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.