Mathematical analysis of the dynamics of a fractional economic cycle model and the existence of solutions by means of fixed point theory

Abstract

This paper proposes a new fractional business cycle model with general investment and variable depreciation rate involving the generalized Hattaf fractional (GHF) derivative. The existence of the model solutions is rigorously established using fixed point theory. Additionally, the mathematical analysis of the dynamics of the proposed fractional model including the stability of economic equilibrium is fully investigated. Furthermore, numerical simulations are presented to illustrate our theoretical results.