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In this manuscript, we examined the controllability and optimal control for fractional stochastic impulsive systems (SISs) with Poisson jumps in finite dimensional space. Some sufficient conditions for controllability results are obtained by using Darbo‐Sadovskii's theorem for higher order damped stochastic system. General conditions are established to study the existence of optimal control for the considered Lagrange problem (LP).

The paper concerned with the controllability of nonlinear fractional noninstantaneous (NI) impulsive integrodifferential stochastic delay system (ISDS). Some sufficient conditions for the controllability of fractional NI impulsive ISDS have been derived by the new approach of measure of noncompactness in finite dimensional space. This NI impulsive ISDS is more reliable for the evolution process in pharmacotherapy. By using Mönch fixed point theorem, existence results have been proved. The result is new in the finite dimensional setting with NI impulse.