Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

• 成果类型: Article
• 署名作者: Monteiro, Noemi Zeraick; dos Santos, Rodrigo Weber; Mazorche, Sandro Rodrigues
• 署名单位: Universidade Federal de Juiz de Fora; Universidade Federal de Juiz de Fora
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-12825
• DOI: 10.1073/pnas.2322424121
• 发表日期: 2024-05-07
• 关键词: systems

摘要

Evolution equations with convolution -type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations. A detailed classification of the memory kernels is presented through parameter analysis. The fractional models we constructed possess distinctive features as they maintain dimensional balance and explicitly relate fractional orders to past data points. Additionally, we illustrate how our models can reproduce the dynamics of COVID-19 infections in Australia, Brazil, and Peru. Our research expands mathematical modeling by presenting a unified framework that facilitates the incorporation of historical data through the utilization of integro-differential equations, fractional or delayed differential equations, as well as classical systems of ordinary differential equations.