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Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

Author

Listed:
  • Hai Zhang
  • Daiyong Wu
  • Jinde Cao

Abstract

We discuss the delay‐independent asymptotic stability of Caputo type fractional‐order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time‐delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:138124
    DOI: 10.1155/2014/138124
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    References listed on IDEAS

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    1. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, February.
    2. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    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, Hindawi, vol. 2010, pages 1-9, June.
    4. Zeynep Orman & Sabri Arik, 2013. "An Analysis of Stability of a Class of Neutral‐Type Neural Networks with Discrete Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Zeynep Orman & Sabri Arik, 2013. "An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, June.
    6. 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, Hindawi, vol. 2010, pages 1-7, August.
    7. Yajing Li & Yejuan Wang, 2013. "Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, November.
    8. 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).
    9. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, November.
    10. R. Sakthivel & P. Revathi & N. I. Mahmudov, 2013. "Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, June.
    12. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    13. Yajing Li & Yejuan Wang, 2013. "Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    14. 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).
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