Fractional kinetic equations: Solutions and applications. (English) Zbl 0933.37029

Summary: Fractional generalization of the diffusion equation includes fractional derivatives with respect to time and coordinate. It had been introduced to describe anomalous kinetics of simple dynamical systems with chaotic motion. We consider a symmetrized fractional diffusion equation with a source and find different asymptotic solutions applying a method which is similar to the method of separation of variables. The method has a clear physical interpretation presenting the solution in a form of decomposition of the process of fractal Brownian motion and Lévy-type process. Fractional generalization of the Kolmogorov-Feller equation is introduced and its solutions are analyzed.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37A60 Dynamical aspects of statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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