Controllability of Hilfer fractional stochastic system with multiple delays and Poisson jumps

This paper introduces a notion of controllability for nonlinear Hilfer fractional stochastic system with multiple delays in control and Poisson jumps. A proper new series of sufficient conditions are derived for the considered system to be controllable by using fixed point technique, fractional calculus and stochastic analysis approach. The obtained result generalizes many results on controllability of stochastic systems and fractional stochastic systems. Finally, an example is provided to show the effectiveness of the achieved theoretical results.