Kebede Shiferaw Geremew, Lakoud Assia Guezane
Mathematics Department, College of Natural Science, Arba Minch University, Arba Minch, Ethiopia.
Mathematics Department, Faculty of Sciences, Badji Mokhtar Annaba University, Annaba, Algeria.
Bound Value Probl. 2023;2023(1):44. doi: 10.1186/s13661-023-01730-5. Epub 2023 Apr 19.
In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo-Fabrizio fractional derivative by dividing the total population into the susceptible population , the vaccinated population , the infected population , the recovered population , and the death class . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo-Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii's fixed point theorem, Schauder's fixed point theorem, the Banach contraction principle, and Ulam-Hyers stability theorem.
在本文中，我们通过将总人口分为易感人群、接种疫苗人群、感染人群、康复人群和死亡类别，考虑了一个涉及卡普托 - 法布里齐奥分数阶导数的冠状病毒病数学模型。本研究的一个核心目标是分析一个涉及卡普托 - 法布里齐奥分数阶微分方程非线性系统的数学模型的解。借助利普希茨假设，我们建立了充分条件和不等式来分析该模型的解。最终，我们运用克拉索谢尔斯基不动点定理、绍德不动点定理、巴拿赫压缩原理和乌拉姆 - 海尔斯稳定性定理来分析所形成的数学模型的解。
