Technical communique: A note on fractional-order derivatives of periodic functions
Technical communique: A note on fractional-order derivatives of periodic functions
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DOI：
10.1016/j.automatica.2010.02.023
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发表时间：
2010-05
期刊：
影响因子：
6.4
通讯作者：
M. Tavazoei
中科院分区：
文献类型：
--
作者：
M. Tavazoei
本文证明，具有特定周期的周期函数的分数阶导数不可能是具有相同周期的周期函数。这里考虑的分数阶导数可以基于每个众所周知的定义Grunwald-Letnikov定义、Riemann-Liouville定义和Caputo定义来获得。这一结论证实了最近发表的一项工作的结果，该工作证明了一类分数阶模型中不存在周期解。此外，基于这一点，可以很容易地证明在更广泛的分数阶模型中不存在周期性响应。最后通过实例说明了论文成果在分数阶系统解分析中的适用性。
In this paper, it is shown that the fractional-order derivatives of a periodic function with a specific period cannot be a periodic function with the same period. The fractional-order derivative considered here can be obtained based on each of the well-known definitions Grunwald–Letnikov definition, Riemann–Liouville definition and Caputo definition. This concluded point confirms the result of a recently published work proving the non-existence of periodic solutions in a class of fractional-order models. Also, based on this point it can be easily proved the absence of periodic responses in a wider class of fractional-order models. Finally, some examples are presented to show the applicability of the paper achievements in the solution analysis of fractional-order systems.