IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i04ns0218348x2340056x.html
   My bibliography  Save this article

Chaotic Behavior Of Financial Dynamical System With Generalized Fractional Operator

Author

Listed:
  • SARA S. ALZAID

    (Research Chair of Financial and Actuarial Studies, Mathematics Department, College of Science, King Saud University, Riyadh 11989, Saudi Arabia†Department of Mathematics, College of Science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia)

  • AJAY KUMAR

    (��Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India)

  • SUNIL KUMAR

    (��Department of Mathematics, College of Science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia‡Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India§Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE¶Department of Mathematics, University Centre for Research and Development, Chandigarh University, Gharuan, Mohali, Punjab, India)

  • BADR SAAD T. ALKAHTANI

    (Research Chair of Financial and Actuarial Studies, Mathematics Department, College of Science, King Saud University, Riyadh 11989, Saudi Arabia†Department of Mathematics, College of Science, King Saud University, P. O. Box 1142, Riyadh 11989, Saudi Arabia)

Abstract

In this paper, we analyzed the chaotic complexity of a financial mathematical model in terms of a new generalized Caputo fractional derivative. There are three components in this nonlinear financial model: price indexes, interest rates, and investment demand. Our analysis is based on applying the fixed point hypothesis to determine the existence and uniqueness of the solutions. The bifurcation of the proposed financial system has been analyzed at various parameters of the system. Dynamical phase portraits of the proposed financial model are demonstrated at various fractional-order values. We investigated the possibility of finding new complex dynamical behavior with generalized Caputo fractional derivative. This economic model is solved numerically using a predictor–corrector (PC) algorithm with a generalized Caputo derivative. This algorithm can be viewed as a non-integer extension of the classical Adams–Bashforth–Moulton (ABM) algorithm. Additionally, this numerical algorithm has been studied for stability. A number of diverse dynamic behaviors have been observed in numerical simulations of the system, including chaos. Over a broad range of system parameters, bifurcation diagrams indicate that the system behaves chaotically.

Suggested Citation

  • Sara S. Alzaid & Ajay Kumar & Sunil Kumar & Badr Saad T. Alkahtani, 2023. "Chaotic Behavior Of Financial Dynamical System With Generalized Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-20.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x2340056x
    DOI: 10.1142/S0218348X2340056X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X2340056X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X2340056X?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:31:y:2023:i:04:n:s0218348x2340056x. 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.