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

Author:

Shah Zahir1ORCID,Bonyah Ebenezer2ORCID,Alzahrani Ebraheem3ORCID,Jan Rashid4ORCID,Aedh Alreshidi Nasser5ORCID

Affiliation:

1. Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, KPK, Pakistan

2. Department of Mathematics Education, University of Education Winneba Kumasi-(Kumasicompus), Kumasi 00233, Ghana

3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

4. Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan

5. Department of Mathematic College of Science Northern Border University, Arar 73222, Saudi Arabia

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.

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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