stability analysis of fractional nonlinear systems, Appl. Math. Lett. (2015), http://dx.Abstract: Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems, however, the well-known Leibniz rule is not suitable for fractional derivatives. This paper deals with fractional nonlinear systems and several algebraic criteria of Mittag-Leffler and asymptotical stability are obtained by using S-procedure and analytical technique. Finally, an example is given to show that it is very convenient to check stability of practical systems by using our proposed methods.

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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 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.