IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i08ns0218348x22402071.html
   My bibliography  Save this article

Chaotic Behavior Of Modified Stretch–Twist–Fold Flow Under Fractal-Fractional Derivatives

Author

Listed:
  • A. DLAMINI

    (Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa)

  • EMILE F. DOUNGMO GOUFO

    (Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa)

  • M. KHUMALO

    (Department of Mathematical Sciences, University of South Africa, Cnr Christian de Wet Road and Pioneer Avenue, Florida 1709, Roodepoort, South Africa)

Abstract

The application of the recently proposed integral and differential operators known as the fractal-fractional derivatives and integrals has opened doors to ongoing research in different fields of science, engineering, and technology. These operators are a convolution of the fractal derivative with the generalized Mittag-Leffler function with Delta-Dirac property, the power law, and the exponential decay law with Delta-Dirac property. In this paper, we aim to extend the work in the literature by applying these operators to a modified stretch–twist–fold (STF) flow based on the STF flow related to the motion of particles in fluids that naturally occur in the dynamo theorem. We want to capture the dynamical behavior of the modified STF flow under these operators. We will present the numerical schemes that can be used to solve these nonlinear systems of differential equations. We will also consider numerical simulations for different values of fractional order and fractal dimension.

Suggested Citation

  • A. Dlamini & Emile F. Doungmo Goufo & M. Khumalo, 2022. "Chaotic Behavior Of Modified Stretch–Twist–Fold Flow Under Fractal-Fractional Derivatives," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-30, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402071
    DOI: 10.1142/S0218348X22402071
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22402071
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22402071?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.

    Citations

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


    Cited by:

    1. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(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:wsi:fracta:v:30:y:2022:i:08:n:s0218348x22402071. 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.