Mathematical modeling and analysis of the dynamics of a nonlinear finance system via Hattaf fractional derivative and fixed point theory

Abstract

In this paper, we propose a new mathematical model that describes the dynamics of a nonlinear finance system. The proposed model is formulated by fractional differential equations (FDEs) involving the generalized Hattaf fractional (GHF) derivative. Firstly, we prove that our fractional model is mathematically and financially well-posed by means of fixed point theory. Additionally, we study the existence of equilibria. Furthermore, the stability analysis of the financial model is carefully studied. Finally, numerical simulations are presented to illustrate our theoretical results.