  The anomalous (i.e. non-Gaussian) dynamics of particles subject to a
deterministic acceleration and a series of 'random kicks' is studied. Based on
an extension of the concept of continuous time random walks to
position-velocity space, a new fractional equation of the Kramers-Fokker-Planck
type is derived. The associated collision operator necessarily involves a
fractional substantial derivative, representing important nonlocal couplings in
time and space. For the force-free case, a closed solution is found and
discussed.
