IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Fractional model equation for anomalous diffusion

Listed author(s):
  • Metzler, Ralf
  • Glöckle, Walter G.
  • Nonnenmacher, Theo F.
Registered author(s):

    In recent years the phenomenon of anomalous diffusion has attracted more and more attention. One of the main impulses was initiated by de Gennes' idea of the “ant in the labyrinth”. Several authors presented asymptotic probability density functions for the location of a random walker on a fractal object. As this density function and the time dependence of its second moment are now well established, a modified diffusion equation providing the correct result is formulated. The parameters of this fractional partial differential equation are uniquely determined by the fractal Hausdorff dimension of the underlying object and the anomalous diffusion exponent. The presented equation reduces exactly to the ordinary isotropic diffusion equation by appropriate choice of the parameters. A closed form solution is given in terms of Fox's H-function. In the asymptotic case a “halved” diffusion equation can be established. Furthermore, the differences to equations considered previously are discussed.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    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

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 211 (1994)
    Issue (Month): 1 ()
    Pages: 13-24

    in new window

    Handle: RePEc:eee:phsmap:v:211:y:1994:i:1:p:13-24
    DOI: 10.1016/0378-4371(94)90064-7
    Contact details of provider: Web page:

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:211:y:1994:i:1:p:13-24. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.