On the linear-quadratic regulator problem in one-dimensional linear fractional stochastic systems

In this paper, for one-dimensional stochastic linear fractional systems in terms of the Riemann-Liouville fractional derivative, the optimal control is derived. It is assumed that the state is completely observable and all the information regarding this is available. The formulation leads to a set of stochastic fractional forward and backward equation in the Riemann-Liouville sense. The proposed method has been checked via some numerical simulations which show the effectiveness of the fractional stochastic optimal algorithm.