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Chaotic Behavior Of Financial Dynamical System With Generalized Fractional Operator

Author

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  • 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
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    Cited by:

    1. Eduardo Reyes de Luna & Andriy Kryvko & Juan B. Pascual-Francisco & Ignacio Hernández & Didier Samayoa, 2024. "Generalized Kelvin–Voigt Creep Model in Fractal Space–Time," Mathematics, MDPI, vol. 12(19), pages 1-13, October.

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