Stability of systems of fractional-order differential equations with caputo derivatives

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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.

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Brandibur, O., Garrappa, R., & Kaslik, E. (2021, April 2). Stability of systems of fractional-order differential equations with caputo derivatives. Mathematics. MDPI AG. https://doi.org/10.3390/math9080914

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