Abstract
Abstract We investigate the physical background and implications of a space- and time-fractional diffusion equation which corresponds to a random walker which combines competing long waiting times and Levy flight properties. Explicit solutions are examined, and the corresponding fractional Fokker–Planck–Smoluchowski equation is presented. The framework of fractional kinetic equations which control the systems relaxation to either Boltzmann–Gibbs equilibrium, or a far from equilibrium Levy form is explored, putting the fractional approach in some perspective from the standard non-equilibrium dynamics point of view, and its generalisation.
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