Modeling the dynamics of business cycle with memory in goods and money markets via the generalized Hattaf fractional derivative

Abstract

In this paper, we propose a new IS-LM model that describes the dynamics of business cycle by taking into account the memory effect in both goods and money markets involving the generalized Hattaf fractional (GHF) derivative. By mains of the fixed point theory, we prove the existence and uniqueness of solutions of our proposed fractional model. Moreover, the existence of the economic equilibrium and its local stability are rigorously established. Finally, numerical simulations are presented to illustrate the effect of memory on the dynamical behavior of the proposed model.