Lyapunov method for nonlinear fractional differential systems with delay

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 exist...

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Bibliographic Details
Published inNonlinear dynamics Vol. 82; no. 1-2; pp. 1015 - 1025
Main Authors Wen, Yanhua, Zhou, Xian-Feng, Zhang, Zhixin, Liu, Song
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2015
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Delay
Differential equations
Dynamical Systems
Engineering
Liapunov functions
Mechanical Engineering
Nonlinear systems
Original Paper
Stability criteria
Vibration
Fractional differential system
Nonlinear
Stability
Delay
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-015-2214-y