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

被引：24

作者：

Brandibur, Oana ^{[1
]}

Garrappa, Roberto ^{[2
,3
]}

Kaslik, Eva ^{[1
]}

机构：

[1] West Univ Timisoara, Dept Math & Comp Sci, Timisoara 300223, Romania

[2] Univ Bari, Dept Math, Via E Orabona 4, I-70126 Bari, Italy

[3] Ist Nazl Alta Matemat Francesco Severi, INdAM Res Grp GNCS, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

MATHEMATICS | 2021年 / 9卷 / 08期

关键词：

fractional differential equations; stability; linear systems; multi-order systems; Mittag– Leffler function;

D O I：

10.3390/math9080914

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：20

共 37 条

[11] Analysis of fractional differential equations with multi-orders [J].