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.
Copyright © 2025 Maha Elkarmouchi, Khalid Hattaf, Jamal Mouline. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Elkarmouchi, K. Hattaf, J. Mouline, Modeling the dynamics of business cycle with memory in goods and money markets via the generalized Hattaf fractional derivative, Adv. Fixed Point Theory 15 (2025), 7. https://doi.org/10.28919/afpt/9075
BibTeX
@article{Elkarmouchi2025,
author = {Elkarmouchi, Maha and Hattaf, Khalid and Mouline, Jamal},
title = {Modeling the dynamics of business cycle with memory in goods and money markets via the generalized Hattaf fractional derivative},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {7},
doi = {10.28919/afpt/9075}
}