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Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems

Author

Listed:
  • Ravi Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
    Mathematics Department, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Snezhana Hristova

    (Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 4000 Plovdiv, Bulgaria)

  • Donal O’Regan

    (School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 CF50 Galway, Ireland)

Abstract

First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional differential equations and we study stability properties by an appropriate modification of the Razumikhin method. Two different types of derivatives of Lyapunov functions are studied: the RL fractional derivative when the argument of the Lyapunov function is any solution of the studied problem and a special type of Dini fractional derivative among the studied problem.

Suggested Citation

  • Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:435-:d:503880
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    References listed on IDEAS

    as
    1. Changpin Li & Deliang Qian & YangQuan Chen, 2011. "On Riemann-Liouville and Caputo Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, March.
    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. Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
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    Cited by:

    1. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2023. "Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory," Mathematics, MDPI, vol. 11(18), pages 1-23, September.

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