IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i05ns0218348x2240182x.html
   My bibliography  Save this article

Chaotic Behavior In Fractional Helmholtz And Kelvin–Helmholtz Instability Problems With Riesz Operator

Author

Listed:
  • KOLADE M. OWOLABI

    (Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria)

  • J. F. GÓMEZ-AGUILAR

    (��CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado, Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México)

  • YELIZ KARACA

    (��University of Massachusetts Medical School, Worcester, MA 01655, USA)

  • YONG-MIN LI

    (�Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China¶Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China)

  • BAHAA SALEH

    (��Department of Mechanical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia)

  • AYMAN A. ALY

    (��Department of Mechanical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the physical patterns of these models arising in hydrodynamics and geophysical fluids. The Laplace and Fourier transform techniques are used to approximate the Riesz fractional operator in a spatial direction. The behaviors of the Helmholtz and Kelvin–Helmholtz equations are observed for some values of fractional power in the regimes, 0 < α ≤ 1 and 1 < α ≤ 2, using different boundary conditions on a square domain in 1D, 2D and 3D (spatial-dimensions). Numerical results reveal some astonishing and very impressive phenomena which arise due to the variations in the initial and source function, as well as fractional parameter α, for subdiffusive and superdiffusive scenarios.

Suggested Citation

  • Kolade M. Owolabi & J. F. Gã“Mez-Aguilar & Yeliz Karaca & Yong-Min Li & Bahaa Saleh & Ayman A. Aly, 2022. "Chaotic Behavior In Fractional Helmholtz And Kelvin–Helmholtz Instability Problems With Riesz Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-19, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x2240182x
    DOI: 10.1142/S0218348X2240182X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X2240182X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X2240182X?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:fracta:v:30:y:2022:i:05:n:s0218348x2240182x. 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: https://www.worldscientific.com/worldscinet/fractals .

    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.