title: Diffusion and relaxation controlled by tempered alpha-stable processes.
abstract: We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha-stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered alpha-stable process provides diffusion (relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation and the Cole-Davidson relaxation function. This model includes subdiffusion as a particular case.
authors.affiliation: Institute of Radio Astronomy, 4 Chervonopraporna Street, 61002 Kharkov, Ukraine. alexstan@ri.kharkov.ua
authors.forename: Aleksander
authors.initials: A
authors.lastname: Stanislavsky
authors.forename: Karina
authors.initials: K
authors.lastname: Weron
authors.forename: Aleksander
authors.initials: A
authors.lastname: Weron