IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v27y2016i01ns0129183116500078.html
   My bibliography  Save this article

Nonlocal electrical diffusion equation

Author

Listed:
  • J. F. Gómez-Aguilar

    (Cátedras CONACYT, Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira, S/N, Col. Palmira C.P. 62490, Cuernavaca, Morelos, México)

  • R. F. Escobar-Jiménez

    (Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México)

  • V. H. Olivares-Peregrino

    (Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México)

  • M. Benavides-Cruz

    (Facultad de Ingeniería en Electrónica y Comunicaciones, Campus)

  • C. Calderón-Ramón

    (Facultad de Ingeniería en Electrónica y Comunicaciones, Campus)

Abstract

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Suggested Citation

  • J. F. Gómez-Aguilar & R. F. Escobar-Jiménez & V. H. Olivares-Peregrino & M. Benavides-Cruz & C. Calderón-Ramón, 2016. "Nonlocal electrical diffusion equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 1-12, January.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:01:n:s0129183116500078
    DOI: 10.1142/S0129183116500078
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183116500078
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183116500078?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.

    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:wsi:ijmpcx:v:27:y:2016:i:01:n:s0129183116500078. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.