منابع مشابه
Parameters of the fractional Fokker-Planck equation
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavytailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability de...
متن کاملFractional Fokker-Planck equation, solution, and application.
Recently, Metzler et al. [Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field, and a Boltzmann thermal heat bath. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordi...
متن کاملFractional Fokker-Planck equation for fractal media.
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 f...
متن کاملFokker–Planck equation with fractional coordinate derivatives
Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...
متن کاملFokker Planck Equation for Fractional Systems
The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usu...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2017
ISSN: 2227-7390
DOI: 10.3390/math5010012