  In this paper, a class of semilinear fractional elliptic equations associated
to the spectral fractional Dirichlet Laplace operator is considered. We
establish the existence of optimal solutions as well as a minimum principle of
Pontryagin type and the first order necessary optimality conditions of
associated optimal control problems. Second order conditions for optimality are
also obtained for $L^{\infty}$ and $L^2-$ local solutions under some structural
assumptions.
