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Anomalous Relaxation and Diffusion Processes in Complex Systems

Gerd Baumann
Organization: Visual Analysis
N. Südland
T. Nonnenmacher
Journal / Anthology

Transport Theory and Statistical Physics
Year: 2000
Volume: 29
Issue: 1-2
Page range: 157-171

Over the last two decades anomalous relaxation and diffusion processes have been studied from both the experimental and theoretical point of view. Anomalous transport processes occur usually in so-called complex, i.e. in disordered systems. Here, we review some recent developments in modeling non-standard relaxation and diffusion equations based on Riemann-Liouville fractional calculus techniques. Closed analytical expressions of the solutions of such fractional differential equations are given in terms of Fox's H-functions. The analytical calculations carried out are fully supported by our Mathematica package.

*Mathematics > Calculus and Analysis > Dynamical Systems