Fractional kinetic equations: solutions and applications

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.