Fractional kinetic equations: solutions and applications
Alexander I. SaichevRadiophysics Department, Nizhniy Novgorod State University, 23 Gagarin Str., Nizhniy Novgorod, 603600, RussiaGeorge M. ZaslavskyCourant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
1997en
ABI
Abstract
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 Levy-type process. Fractional generalization of the Kolmogorov-Feller equation is introduced and its solutions are analyzed. (c) 1997 American Institute of Physics.
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Cited by 30 references