  We used a complete tight-binding band structure of graphene nanoribbon to
obtain, for the first time, analytical techniques for observing photon assisted
transport, and dynamic localization of electrons in the graphene nanoribbons.
When the ribbons are subject to a multi-frequency dc-ac field, photon assisted
replicas show up at rather strong drive force. The strong dependence of the
photon peaks on ac amplitudes allow for high-harmonic dynamic oscillations at
these amplitudes. We identified regions of positive differential conductivity
where a nanoelectronic graphene device may be operated as a small signal
amplifier. Our research has also reveal another quantum mechanical phenomenon,
fractional photon assisted transport, when the stark factor $r > 1$.
