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Fokker–Planck equation with fractional coordinate derivatives

Author

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  • Tarasov, Vasily E.
  • Zaslavsky, George M.

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.

Suggested Citation

  • Tarasov, Vasily E. & Zaslavsky, George M., 2008. "Fokker–Planck equation with fractional coordinate derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6505-6512.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:26:p:6505-6512
    DOI: 10.1016/j.physa.2008.08.033
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    References listed on IDEAS

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    1. Yanovsky, V.V. & Chechkin, A.V. & Schertzer, D. & Tur, A.V., 2000. "Lévy anomalous diffusion and fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 13-34.
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    Cited by:

    1. Habibi, Noora & Lashkarian, Elham & Dastranj, Elham & Hejazi, S. Reza, 2019. "Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker–Planck equations for special stochastic process in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 750-766.
    2. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.

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