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Fokker-Planck equation with fractional coordinate derivatives |
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| Authors: | Vasily E Tarasov George M Zaslavsky |
| Institution: | a Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA b Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991, Russia c Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA |
| Abstract: | 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<α<2. |
| Keywords: | Fractional kinetics Fractional derivatives Long-range interaction Fokker-Planck equation Kolmogorov-Feller equation |
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