  We formulate the Kohn-Sham equations for the fractional quantum Hall effect
by mapping the original electron problem into an auxiliary problem of composite
fermions that experience a density dependent effective magnetic field.
Self-consistent solutions of the KS equations demonstrate that our formulation
captures not only configurations with non-uniform densities but also
topological properties such as fractional charge and fractional braid
statistics for the quasiparticles excitations. This method should enable a
realistic modeling of the edge structure, the effect of disorder, spin physics,
screening, and of fractional quantum Hall effect in mesoscopic devices.
