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Lyapunov method for nonlinear fractional differential systems with delay

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Abstract

This paper deals with the stability of nonlinear fractional differential systems with delay. Based on the Lyapunov functional method and the Lyapunov function method, respectively, several stability criteria including Razumikhin-type stability criteria are derived, which are extensions of some existed results of the Hale and Verduyn Lunel (Introduction to functional differential equations. Springer, Berlin, 1993), Aguila-Camacho et al. (Commun Nonlinear Sci Numer Simul 19, 2951–2957, 2014) and Zhou et al. (Appl Math Lett 28, 25–29, 2014). In addition, some examples are provided to illustrate the applications of these criteria. Numerical simulations show the validity of our results.

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Acknowledgments

The authors would like to thank the reviewers for their valuable comments and suggestions, which improve the quality of this paper. This paper is supported by National Natural Science Foundation of China (11371027, 11471015), Natural Science Foundation of Anhui Province (1508085MA01), Research Fund for Doctoral Program of Higher Education of China (20123401120001, 20133401120013), Natural Science Foundation for Colleges and Universities of Anhui Province (KJ2012A032) and The Program of Academic Innovation Research for Postgraduate of Anhui University (yfc100013).

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230039, China

    Yanhua Wen, Xian-Feng Zhou, Zhixin Zhang & Song Liu

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  1. Yanhua Wen
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  2. Xian-Feng Zhou
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  3. Zhixin Zhang
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  4. Song Liu
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Correspondence to Xian-Feng Zhou.

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Wen, Y., Zhou, XF., Zhang, Z. et al. Lyapunov method for nonlinear fractional differential systems with delay. Nonlinear Dyn 82, 1015–1025 (2015). https://doi.org/10.1007/s11071-015-2214-y

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