A study on fractional order financial model by using Caputo–Fabrizio derivative

Abstract

This paper aims to provide an understanding of the dynamics and behavior of the financial model in the context of fractional differential equations. The model explores the interactions and connections among four key financial variables: interest rates, investment demand, price index, and savings amounts. We establish the existence of unique solution for the fractional financial model and stability of the model using iterative approach by employing Banach’s fixed point theory. A numerical method is carried out to perform the numerical simulation of the Caputo–Fabrizio financial model. The work capitalizes on the insights gained by scrutinizing the repercussions stemming from variations in model parameters on the dynamics of the solutions obtained through our numerical scheme. Our findings highlight that the interplay among diverse financial components can lead to chaotic behavior in specific scenarios.

Keywords

• Financial model
• Fixed point theory
• Sumudu transform
• Numerical simulation