  We quantum mechanically analyze the fractional quantum Hall effect in
graphene. This will be done by building the corresponding states in terms of a
potential governing the interactions and discussing other issues. More
precisely, we consider a system of particles in the presence of an external
magnetic field and take into account of a specific interaction that captures
the basic features of the Laughlin series \nu={1\over 2l+1}. We show that how
its Laughlin potential can be generalized to deal with the composite fermions
in graphene. To give a concrete example, we consider the SU(N) wavefunctions
and give a realization of the composite fermion filling factor. All these
results will be obtained by generalizing the mapping between the
Pauli--Schr\"odinger and Dirac Hamiltonian's to the interacting particle case.
Meantime by making use of a gauge transformation, we establish a relation
between the free and interacting Dirac operators. This shows that the involved
interaction can actually be generated from a singular gauge transformation.
