Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps

The problem of approximate controllability is investigated in this paper for a class of fractional stochastic differential equations driven by fractional Brownian motion with non‐instantaneous impulses and Poisson jumps. The results are obtained by employing the η ‐resolvent family and Krasnoselskii's fixed point theorem. Further, we derive the trajectory controllability for the proposed stochastic control system. Finally, an example is provided to illustrate the obtained theory.