IDEAS home Printed from https://ideas.repec.org/a/wly/complx/v2022y2022i1n8113760.html

Chaotic Phenomena and Oscillations in Dynamical Behaviour of Financial System via Fractional Calculus

Author

Listed:
  • Zahir Shah
  • Ebenezer Bonyah
  • Ebraheem Alzahrani
  • Rashid Jan
  • Nasser Aedh Alreshidi

Abstract

In this research work, we formulate the phenomena of the financial system in the fractional framework to describe the complex nature of finance. The basic definitions and ideas of the Caputo‐Fabrizio fractional operator are listed. We introduce a novel numerical technique for the dynamical behaviour of our fractional model. The oscillatory and chaotic behaviour of the model is studied with the variation of various input parameters on the model. We have shown that there exists strong oscillatory and chaotic behaviour in the system; moreover, we highlighted the impact of fractional‐order parameter on the model. The conditions for the local complex behaviour of the system are analyzed with the impact of certain parameters on the macroeconomic. Our findings suggest that the values of initial conditions, fractional order, and input parameters can lessen the chaos of the proposed financial system.

Suggested Citation

  • Zahir Shah & Ebenezer Bonyah & Ebraheem Alzahrani & Rashid Jan & Nasser Aedh Alreshidi, 2022. "Chaotic Phenomena and Oscillations in Dynamical Behaviour of Financial System via Fractional Calculus," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:8113760
    DOI: 10.1155/2022/8113760
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/8113760
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/8113760?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
    ---><---

    References listed on IDEAS

    as
    1. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    2. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Oana Brandibur & Eva Kaslik & Dorota Mozyrska & Małgorzata Wyrwas, 2020. "Stability Results for Two-Dimensional Systems of Fractional-Order Difference Equations," Mathematics, MDPI, vol. 8(10), pages 1-17, October.
    4. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
    5. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Patience Pokuaa Gambrah & Davidon Jani & Kwasi Frempong Sarfo & Herman Matondo Mananga & Forster Owusu, 2025. "Mathematical Modeling of Divorce Incidence With Social Media Influence Using Caputo Fractional Derivative," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    2. Özüm Emre Aşırım & Tunç Murat İlgar & Adil Aşırım & Murat Adil Salepçioğlu & Ece Asirim, 2026. "Modeling foreign exchange rates as stochastic difference equations with minimum uncertainty for prediction analysis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 12(1), pages 1-34, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    2. Li-xin Yang & Wan-sheng He, 2013. "Adaptive Q‐S Synchronization of Fractional‐Order Chaotic Systems with Nonidentical Structures," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    4. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    5. Mohammad Izadi & Şuayip Yüzbaşi & Samad Noeiaghdam, 2021. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    6. Ding, Yuting & Jiang, Weihua & Wang, Hongbin, 2012. "Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1048-1057.
    7. José M. Gaspar, 2018. "Erratum to “Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand‐Aggregate Supply Model with Matlab”," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    8. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    9. Phukan, Animesh & Sarmah, Hemanta Kumar, 2025. "Bifurcation analysis of a non linear 6D financial system with three time delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    10. Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    11. Kenshiro Ninomiya, 2025. "Debt burdens of governments and firms and the countercyclical fiscal policy," Evolutionary and Institutional Economics Review, Springer, vol. 22(1), pages 265-281, April.
    12. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    13. Lahoucine Tadoummant & Hammad Khalil & Rachid Echarggaoui & Sarah Aljohani & Nabil Mlaiki, 2025. "A novel method for approximate solution of two point non local fractional order coupled boundary value problems," PLOS ONE, Public Library of Science, vol. 20(7), pages 1-31, July.
    14. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    15. Akio Matsumoto & Ferenc Szidarovszky, 2016. "Delay Dynamics in a Classical IS-LM Model with Tax Collections," Metroeconomica, Wiley Blackwell, vol. 67(4), pages 667-697, November.
    16. Fanti, Luciano & Manfredi, Piero, 2007. "Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 736-744.
    17. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    18. Murakami, Hiroki, 2014. "Keynesian systems with rigidity and flexibility of prices and inflation–deflation expectations," Structural Change and Economic Dynamics, Elsevier, vol. 30(C), pages 68-85.
    19. Yan Qiao & Chong Li & Azmat Ullah Khan Niazi & Xin Pang, 2025. "Fractional Age‐Structured Modeling of Measles: Application of Inverse Methods," Complexity, John Wiley & Sons, vol. 2025(1).
    20. Zemtchou, Francis Rolphe & Mabekou Takam, Jeanne Sandrine & Louodop Fotso, Patrick Hervé & Talla, Pierre Kisito, 2025. "Piezoelectric energy harvesting from beam vibrations induced by an aerodynamic force generated by a fluctuating wind," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:complx:v:2022:y:2022:i:1:n:8113760. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/8503 .

    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.