Approximate controllability for Hilfer fractional stochastic differential systems of order 1<μ<2

In this paper, we analyse the approximate controllability of Hilfer fractional stochastic differential systems of order 1<μ<2 in Hilbert spaces. The primary findings are carried out by using fractional calculus, stochastic analysis theory, cosine family, and Schauder's fixed point theorem. In particular, we draw a new set of sufficient conditions for the approximate controllability of Hilfer fractional stochastic differential equations of order 1<μ<2 under the assumption that the corresponding linear system is approximately controllable. In the end, an example is provided to illustrate the derived theory.