IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i26p6505-6512.html
   My bibliography  Save this article

Fokker–Planck equation with fractional coordinate derivatives

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108007528
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2008.08.033?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lubashevsky, Ihor, 2013. "Equivalent continuous and discrete realizations of Lévy flights: A model of one-dimensional motion of an inertial particle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2323-2346.
    2. Oraby, T. & Suazo, E. & Arrubla, H., 2023. "Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Bai, Zhan-Wu & Hu, Meng, 2015. "Escape rate of Lévy particles from truncated confined and unconfined potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 332-339.
    4. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    5. Evangelista, L.R. & Lenzi, E.K. & Barbero, G. & Scarfone, A.M., 2024. "On the Einstein–Smoluchowski relation in the framework of generalized statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:387:y:2008:i:26:p:6505-6512. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.