Approximate controllability of fractional stochastic differential equations driven by mixed fractional Brownian motion via resolvent operators

In this manuscript, we investigate the approximate controllability of a class of fractional stochastic differential equations driven by mixed fractional Brownian motion in Hilbert space with Hurst parameter H∈(12,1). The main results are obtained by employing fractional calculus, analytic resolvent operators and with the help of Schaefer's fixed-point theorem under the assumption that the corresponding linear system is approximately controllable. Finally, in order to validate the obtained theoretical results, an illustrative example is provided.