  Dynamics of many-body Hamiltonian systems with long range interactions is
studied, in the context of the so called $\alpha-$HMF model. Building on the
analogy with the related mean field model, we construct stationary states of
the $\alpha-$HMF model for which the spatial organization satisfies a
fractional equation. At variance, the microscopic dynamics turns out to be
regular and explicitly known. As a consequence, dynamical regularity is
achieved at the price of strong spatial complexity, namely a microscopic
inhomogeneity which locally displays scale invariance.
