论文标题
Lyapunov的生物学分数系统功能：方法和应用
Lyapunov functions for fractional-order systems in biology: methods and applications
论文作者
论文摘要
We prove new estimates of the Caputo derivative of order $α\in (0,1]$ for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a更精确地研究了分数细胞模型，我们构建了合适的Lyapunov功能，以证明两个模型的自由和地方性平衡的全局稳定性，并且还执行了一些数值模拟来确认我们的选择。
We prove new estimates of the Caputo derivative of order $α\in (0,1]$ for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.
