Fractional Fokker-Planck Equation for Fractal Media

Details Fractional Fokker-Planck Equation for Fractal Media Fractional Fokker-Planck Equation for Fractal Media

2006-02-14

arxiv.org/abs/nlin/0602029v1

Chaos 15 (2005) 023102

Nonlinear Sciences

Chaotic Dynamics

17 pages

Scientific paper

We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived from the fractional Chapman-Kolmogorov equation. Using the Fourier transform, we get the Fokker-Planck-Zaslavsky equations that have fractional coordinate derivatives. The Fokker-Planck equation for the fractal media is an equation with fractional derivatives in the dual space.

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