In this paper, a new approach is proposed for stability analysis of fractional stochastic systems. By extending the concept of infinitesimal generator using the fractional Ito formula, it becomes possible to apply it in fractional stochastic systems for stability analysis by Lyapunov functions. Thereafter, the presented stability criterion is utilized to develop the sliding mode control scheme for fractional stochastic systems with state delay.  The proposed design method ensures that the state trajectories reach the sliding surface in finite time with probability one. Stability analysis of the system at sliding mode is executed using the given fractional infinitesimal generator and the stability conditions are given in the form of linear matrix inequalities. To illustrate the efficiency of the results, the application of the method is presented for the pitch control of a variable speed wind turbine.