On the fractional Lyapunov exponent for Hadamard-type fractional differential system
On the fractional Lyapunov exponent for Hadamard-type fractional differential system
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关于Hadamard型分数阶微分系统的分数阶Lyapunov指数
DOI：
10.1063/5.0131661
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Bowen Wu
中科院分区：
文献类型：
--
作者：
Li Ma;Bowen Wu
针对Hadamard型分数阶微分系统（HTFDS），给出了分数阶李雅普诺夫指数的定义.首先，讨论了非自治HTFDS解的连续依赖性。然后，利用连续相关性和变分原理的结果，建立了一个与Mittag-Leffler特征函数和分数阶数都具有良好相关性的分数阶李雅普诺夫指数来表征HTFDS的混沌动力学行为.随后，一般HTFDS的分数李雅普诺夫指数的上界估计考虑其变化系统。最后，给出了一个必要的例子来验证我们的主要结果，这也表明不同类型的分数阶系统确实具有不同的李雅普诺夫指数。
This paper is mainly dedicated to defining an adequate notion of fractional Lyapunov exponent to the Hadamard-type fractional differential system (HTFDS). First, the continuous dependence of the solution to a nonautonomous HTFDS is discussed. Then, to characterize the specific chaotic dynamics of the HTFDS, a novel fractional Lyapunov exponent well correlated with both the Mittag–Leffler characteristic function and the fractional order is well established by the aid of the results of continuous dependence and variational principle to the HTFDS. Subsequently, the upper bound of fractional Lyapunov exponents for the general HTFDS is estimated on account of its variation system. Finally, an indispensable illustration is presented to verify our main results, which also infers that different kinds of fractional systems share different Lyapunov exponents indeed.