Comments on "Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks"
Comments on "Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks"
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DOI：
10.1016/j.cnsns.2015.01.013
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发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
N. Aguila-Camacho;M. Duarte-Mermoud
中科院分区：
文献类型：
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作者：
N. Aguila-Camacho;M. Duarte-Mermoud
这封信显示了论文中报告的分数阶导数链规则的错误应用(Chen等人，2014)。由于这种误导性的应用，Chen等人(2014)中的定理2和定理5的证明是不正确的。然而，上述定理2是根据文献中已有的结果得出的直接结论(Jarad等人，2013；Matignon 1996)，因此没有必要证明它，正如这封信中所述。同样，虽然Chen等人对定理5的证明也是如此。(2014)是无效的，定理5确实是正确的，并就如何证明它向作者提出了建议。此外，这封信还表明，Chen等人(2014)中提出的定理1也是文献(Jarad等人，2013；斯洛廷和李，1999)中众所周知的结果的直接结论，因此这个结果也不需要证明。
This letter shows an incorrect application of the chain rule for fractional order derivatives reported in paper (Chen et al., 2014). Due to this misleading application, the proof of Theorem 2 and Theorem 5 in Chen et al., (2014) are incorrect. However, the mentioned Theorem 2 is a straightforward conclusion from results already available in literature (Jarad et al., 2013; Matignon 1996), and consequently there is no need to prove it, as it is stated in this letter. In the same way, although the proof of Theorem 5 in Chen et al. (2014) is not valid, Theorem 5 is indeed true, and a recommendation as to how to prove it is made to the authors. Besides, this letter shows that the proposed Theorem 1 in Chen et al., (2014) is also a straightforward conclusion from well known results available in literature (Jarad et al., 2013; Slotine and Li, 1999), so no demonstration is needed for this result neither.