We consider a bilinear optimal control for an evolution equation involving space fractional Laplacian operator of order 0 < s < 1. We first give some existence and uniqueness results for different equations considered in our work. Then, we consider an optimal control problem which consist to bring the state of our model at final time to a desired state. We show that this optimal control problem has a solution that we characterize using the Euler-Lagrange first order optimality conditions. Finally, we establish some weak maximum principle results that allow us to prove the uniqueness of the optimal control.