An investigation into the controllability of multivalued stochastic fractional differential inclusions

This research aims to investigate the approximate controllability of multivalued impulsive stochastic fractional differential inclusions in Hilbert space with $\mathrm{ABC}$ fractional-order derivatives. First, we confirm the existence of mild solutions for the proposed control system using stochastic analysis, resolvent operator theory, and the fixed point technique. Secondly, we discuss a new set of sufficient conditions for the approximate controllability of the systems. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the obtained results.