The continuous time random walk (CTRW) in a homogeneous velocity field and in arbitrary force fields is studied. Within the extended CTRW scheme, anomalous transport properties due to long-tailed waiting time or jump length distributions are consistently introduced. The connections with generalised diffusion equations in a potential field are discussed, these equations being of fractional order. In particular, the problems of a constant and a Hookean (linear) force, i.e., of a linear and a parabolic potential, are worked out.

• Received 9 April 1998

DOI:https://doi.org/10.1103/PhysRevE.58.1621