  We prove the existence and uniqueness of invariant measures for the
fractional stochastic Burgers equation (FSBE) driven by fractional power of the
Laplacian and space-time white noise. We show also that the transition measures
of the solution converge to the invariant measure in the norm of total
variation. To this end we show first two results which are of independent
interest: that the semigroup corresponding to the solution of the FSBE is
strong Feller and irreducible.
