Abstract This paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

中文翻译：

---

关于 Hadamard 型分数微分系统的动力学

摘要 本文从两个方面对Hadamard型分数阶微分系统(HTFDSs)的动力学进行了研究。一方面，证明了在某些函数空间中考虑的一般HTFDS的非平凡周期解不存在，并讨论了Hadamard型分数阶微分算子的相应特征函数。另一方面，通过广义 Gronwall 型不等式，我们估计了 HTFDS 的 Lyapunov 指数的界限。此外，还通过数值模拟来验证所获得的理论结果。