Controllability of fractional order stochastic differential inclusions with fractional Brownian motion in finite dimensional space

In this paper, sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion U+0028 fBm U+0029 via fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case. The controllability Grammian matrix is defined by using Mittag-Leffler matrix function. Finally, a numerical example is presented to illustrate the efficiency of the obtained theoretical results.