December 2000 - 001202
Review Paper by Metzler and Klafter

An interesting review-paper on Fractional Calculus Modelling is recentely appeared on a Physics prestigious journal:
R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, Vol. 339, pp. 1-77 (2000) (www.elsevier.com/locate/physrep)

ABSTRACT

Fractional kinetic equations of the diffusion, diffusion-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 diffusion and non-exponential 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.

PACS: 05.40.a; 05.40.Fb (Random walks and Levy flights); 02.50.Ey (Stochastic processes)

Keywords: Anomalous diffusion; Fractional diffusion equation; Fractional Fokker-Planck equation; Anomalous relaxation; Mittag-Leffler relaxation; Dynamics in complex systems