  By means of variational methods, in this paper, we establish sharp existence
results for solutions of the master equations governing `fractional multiple
vortices.' In the doubly periodic situation, the conditions for existence are
both necessary and sufficient and give the upper bounds for the vortex numbers
in terms of the size of the periodic cell domain. In the planar situation,
there is no restriction on the vortex numbers. In both situations, the
solutions are uniquely determined by the prescribed locations and the local
winding numbers of the vortices.
