Fokker-Planck equation with fractional coordinate derivativesстатья
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Аннотация: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 averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1 < alpha < 2. (c) 2008 Elsevier B.V. All rights reserved.