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Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

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Abstract

The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

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Acknowledgements

Research was partially supported by Fund MU17-FMI-007, University of Plovdiv Paisii Hilendarski.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA

    Ravi Agarwal

  2. Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL, 32901, USA

    Ravi Agarwal

  3. Department of Applied Mathematics and Modeling, University of Plovdiv Paisii Hilendarski, Plovdiv, Bulgaria

    Snezhana Hristova

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Ravi Agarwal
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  2. Snezhana Hristova
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  3. Donal O’Regan
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Correspondence to Ravi Agarwal.

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Agarwal, R., Hristova, S. & O’Regan, D. Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays. Differ Equ Dyn Syst 30, 513–534 (2022). https://doi.org/10.1007/s12591-018-0434-6

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  • DOI: https://doi.org/10.1007/s12591-018-0434-6

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