Institute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
Sci Rep. 2024 Apr 5;14(1):8058. doi: 10.1038/s41598-024-58132-5.
In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.
在本文中，我们提出了一个分数阶数学模型，通过使用分数阶算子的广义形式来解释胰高血糖素在维持人体血糖水平中的作用。利用不动点理论和系统的 Lipschitz 条件构建了结果的存在性、有界性和正定性。还使用 Lyapunov 一阶导数函数进行了全局稳定性分析。在 Mittage-Leffler 核的帮助下，通过拉格朗日插值法推导出分数阶系统的数值模拟。针对不同初始条件下的正常人和 1 型糖尿病得出了结果，这些结果支持了理论观察。这些结果在闭环设计意义上对葡萄糖-胰岛素-胰高血糖素系统起着重要作用，有助于开发人工胰腺来控制社会中的糖尿病。
