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

Oana Brandibur, Roberto Garrappa and Eva Kaslik
Additional contact information
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
Eva Kaslik: Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timisoara, Romania

Mathematics, 2021, vol. 9, issue 8, 1-20

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.

Keywords: fractional differential equations; stability; linear systems; multi-order systems; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/8/914/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/8/914/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:8:p:914-:d:539806

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().