We are concerned with the fractional order equations with Hartree type
nonlinearity and its equivalent integral equations. We first prove a regularity
result which indicates that weak solutions are smooth. Then, by applying the
method of moving planes in integral forms, we prove that positive solutions of
integral equations are radially symmetric about some point and derive the
explicit forms of solutions. As a consequence, we also derive the best constants
in the corresponding Hardy-Littlewood-Sobolev inequalities.