Fractional kinetic equations of the di!usion, di!usion}advection, and Fokker}Planck type are presented
as a useful approach for the description of transport dynamics in complex systems which are governed by
anomalous di!usion and nonexponential relaxation patterns. These fractional equations are derived
asymptotically from basic random walk models, and from a generalised master equation. Several physical
consequences are discussed which are relevant to dynamical processes in complex systems. Methods of
solution are introduced and for some special cases exact solutions are calculated. This report demonstrates
that fractional equations have come of age as a complementary tool in the description of anomalous
transport processes.
2000 Elsevier Science B.V. All rights reserved.
