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Review

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

1
Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timisoara, Romania
2
Department of Mathematics, University of Bari, Via E. Orabona 4, 70126 Bari, Italy
3
Member of the INdAM Research Group GNCS, Istituto Nazionale di Alta Matematica “Francesco Severi”, Piazzale Aldo Moro 5, 00185 Rome, Italy
*
Author to whom correspondence should be addressed.
Academic Editor: Fasma Diele
Mathematics 2021, 9(8), 914; https://doi.org/10.3390/math9080914
Received: 5 March 2021 / Revised: 18 April 2021 / Accepted: 19 April 2021 / Published: 20 April 2021
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. View Full-Text
Keywords: fractional differential equations; stability; linear systems; multi-order systems; Mittag–Leffler function fractional differential equations; stability; linear systems; multi-order systems; Mittag–Leffler function
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MDPI and ACS Style

Brandibur, O.; Garrappa, R.; Kaslik, E. Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives. Mathematics 2021, 9, 914. https://doi.org/10.3390/math9080914

AMA Style

Brandibur O, Garrappa R, Kaslik E. Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives. Mathematics. 2021; 9(8):914. https://doi.org/10.3390/math9080914

Chicago/Turabian Style

Brandibur, Oana, Roberto Garrappa, and Eva Kaslik. 2021. "Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives" Mathematics 9, no. 8: 914. https://doi.org/10.3390/math9080914

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