  This paper deals with the Cauchy-Dirichlet problem for the fractional
Cahn-Hilliard equation. The main results consist of global (in time) existence
of weak solutions, characterization of parabolic smoothing effects (implying
under proper condition eventual boundedness of trajectories), and convergence
of each solution to a (single) equilibrium. In particular, to prove the
convergence result, a variant of the so-called \L ojasiewicz-Simon inequality
is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic
(but $C^1$) nonlinearities.
