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Mittag‐Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

Author

Listed:
  • S. J. Sadati
  • D. Baleanu
  • A. Ranjbar
  • R. Ghaderi
  • T. Abdeljawad (Maraaba)

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

Suggested Citation

  • S. J. Sadati & D. Baleanu & A. Ranjbar & R. Ghaderi & T. Abdeljawad (Maraaba), 2010. "Mittag‐Leffler Stability Theorem for Fractional Nonlinear Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:108651
    DOI: 10.1155/2010/108651
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    References listed on IDEAS

    as
    1. Shaher Momani & Samir Hadid, 2004. "Lyapunov stability solutions of fractional integrodifferential equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-5, January.
    2. D. Baleanu & S. J. Sadati & R. Ghaderi & A. Ranjbar & T. Abdeljawad (Maraaba) & F. Jarad, 2010. "Razumikhin Stability Theorem for Fractional Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, June.
    3. D. Baleanu & S. J. Sadati & R. Ghaderi & A. Ranjbar & T. Abdeljawad (Maraaba) & F. Jarad, 2010. "Razumikhin Stability Theorem for Fractional Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Hai Zhang & Daiyong Wu & Jinde Cao, 2014. "Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Yang Zhao & Dumitru Baleanu & Mihaela Cristina Baleanu & De-Fu Cheng & Xiao-Jun Yang, 2013. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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