Abstract
Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time‐delay systems for Caputo′s derivative, and we proved two theorems for Mittag‐Leffler stability of the fractional nonlinear time delay systems.Erratum to “Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay”dx.doi.org/10.1155/2011/304352
Highlights
During the last decade the fractional calculus 1–5 has gained importance in both theoretical and applied aspects of several branches of science and engineering 6–15
Some literatures published about stability of fractional-order linear time delay systems can be found in 19, 20
We are often interested in the set of continuous function mapping −r, 0 to Rn, for which we simplify the notation to C C −r, 0, Rn
Summary
During the last decade the fractional calculus 1–5 has gained importance in both theoretical and applied aspects of several branches of science and engineering 6–15. For the time delay case we mention the seminal works on the applicability of Lyapunov’s second method 16, 17. Since 1950s different types of the Lyapunov functions have been proposed for the stability analysis of delay systems, see the pioneering works of Razumikhin and Krasovski. In the base of Lyapunov’s second method, some work has been done in the field of stability of fractional order nonlinear systems without delay 21–23. Razumikhin theorem for the fractional nonlinear time-delay systems was extended recently in 24. The main aim of this paper is to establish the Mittag-Leffler stability theorem for fractional order nonlinear time-delay systems.
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