  We provide an existence result for stationary fractional mean field game
systems, with fractional exponent greater than 1/2. In the case in which the
coupling is a nonlocal regularizing potential, we obtain existence of solutions
under general assumptions on the Hamiltonian. In the case of local coupling, we
restrict to the subcritical regime, that is the case in which the diffusion
part of the operator dominates the Hamiltonian term. We consider both the case
of local bounded coupling and of local unbounded coupling with power-type
growth. In this second regime, we impose some conditions on the growth of the
coupling and on the growth of the Hamiltonian with respect to the gradient
term.
