  We numerically compute the density of states (DOS) of interacting disordered
zigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractional
edge charges. The computed Hartree-Fock DOS is linear at the critical disorder
strength where the gap vanishes. This implies an $I\mbox{-}V$ curve of
$I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence of
fractional charges in interacting disordered ZGNR. We show that even a weak
disorder potential acts as a singular perturbation on zigzag edge electronic
states, producing drastic changes in the energy spectrum. Spin-charge
separation and fractional charges play a key role in the reconstruction of edge
antiferromagnetism. Our results show that an interacting disordered ZGNR is a
topologically ordered Mott-Anderson insulator.
