Accelerating through a potential landscape: A fractional dynamics approachto enhanced motion in an external force field?

We address the question of describing enhanced transport in an external for ce field close to thermal equilibrium, within the framework of fractional d ynamics. We demonstrate that in the overdamped regime inconsistencies arise , in the existence of negative regions of the propagator. Despite of this o bservation, we claim that this approach might be useful for the long time d escription of such systems.