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Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives

Author

Listed:
  • Oana Brandibur

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timisoara, Romania)

  • Roberto Garrappa

    (Department of Mathematics, University of Bari, Via E. Orabona 4, 70126 Bari, Italy
    Member of the INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale Aldo Moro 5, 00185 Rome, Italy)

  • Eva Kaslik

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timisoara, Romania)

Abstract

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on stability of single-order systems, for which a different proof is provided together with a clarification of a limit case, the investigation is moved towards multi-order systems as well. Due to the key role of the Mittag–Leffler function played in representing the solution of linear systems of FDEs, a detailed analysis of the asymptotic behavior of this function and of its derivatives is also proposed. Some numerical experiments are presented to illustrate the main results.

Suggested Citation

  • Oana Brandibur & Roberto Garrappa & Eva Kaslik, 2021. "Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:914-:d:539806
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    References listed on IDEAS

    as
    1. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    2. Margarita Rivero & Sergei V. Rogosin & José A. Tenreiro Machado & Juan J. Trujillo, 2013. "Stability of Fractional Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
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    1. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.

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