  We investigate magnetoplasmon dynamics localized on the edges of graphene
vortex Hall fluid. The vortex matter captures an anomalous term that causes
vortex localization near fluid boundary and creates a double boundary layer,
$\Delta_0\propto (\beta-1)\ell_B$ with $\beta$ being filling factor. The term
also has qualitative effect on resonant excitations of edge magnetoplasmons. We
found that for sharp edges under experimental conditions, graphene Edge
Magnetoplasmon (EMP) resonances have similar behavior as in recent experiments.
Gradual distinctions arise for smooth edges in the presence of the anomalous
term, where a weak EMP peak appear. The second peak becomes well noticed as the
smoothness is increased. We identified the resonant mode as an Inter-EMP. It
originates from the oscillations of charges in the inner boundary of the double
layer. The present observation brings to light the direct cause of Inter-EMP
which remained to be detected in graphene experiments.
