This article aims to discuss the approximate controllability of multivalued impulsive stochastic fractional differential equations with ABC derivatives in Hilbert space. Firstly, with the help of stochastic analysis, theory of resolvent operators and the fixed point technique, we confirm the existence of mild solutions for the proposed control system. Secondarily, we show that the proposed system of equations is approximately controllable under a certain hypothesis. To confirm the applicability of the obtained results, an example is provided at the end of this paper.

In this article, we discuss the controllability and stability of Hilfer fractional evolution equations in Banach space. We derive these results by first proving the existence and uniqueness of mild solutions for proposed system of equations. Existence and uniqueness results are obtained with the help of theory of propagation family, techniques of measure of non-compactness and fixed point theorem. An example is also given for the demonstration of obtained results.