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Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method

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  • Ravi Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA)

  • Snezhana Hristova

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

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, National University of Ireland, H91 TK33 Galway, Ireland)

Abstract

Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and considered, and also some sufficient conditions to guarantee stability are presented. The study is based on the application of Lyapunov like functions and their generalized proportional Caputo fractional derivatives among solutions of the studied system where appropriate Razumikhin like conditions are applied (appropriately modified in connection with the fractional derivative considered). The theory is illustrated with several nonlinear examples.

Suggested Citation

  • Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2022. "Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1849-:d:826171
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
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