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.
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页数：20
相关论文
共 37 条
[1]   Cauchy problems for some classes of linear fractional differential equations [J].
Atanackovic, Teodor ;
Dolicanin, Diana ;
Pilipovic, Stevan ;
Stankovic, Bogoljub .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2014, 17 (04) :1039-1059
[2]   Coprime factorizations and stability of fractional differential systems [J].
Bonnet, C ;
Partington, JR .
SYSTEMS & CONTROL LETTERS, 2000, 41 (03) :167-174
[3]   EXACT STABILITY AND INSTABILITY REGIONS FOR TWO-DIMENSIONAL LINEAR AUTONOMOUS MULTI-ORDER SYSTEMS OF FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS [J].
Brandibur, Oana ;
Kaslik, Eva .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2021, 24 (01) :225-253
[4]   Stability analysis of multi-term fractional-differential equations with three fractional derivatives [J].
Brandibur, Oana ;
Kaslik, Eva .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (02)
[5]   Stability of two-component incommensurate fractional-order systems and applications to the investigation of a FitzHugh-Nagumo neuronal model [J].
Brandibur, Oana ;
Kaslik, Eva .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (17) :7182-7194
[6]   Stability properties of a two-dimensional system involving one Caputo derivative and applications to the investigation of a fractional-order Morris-Lecar neuronal model [J].
Brandibur, Oana ;
Kaslik, Eva .
NONLINEAR DYNAMICS, 2017, 90 (04) :2371-2386
[7]  
Brunner H., 2017, Cambridge Monographs on Applied and Computational Mathematics
[8]   Stability properties of two-term fractional differential equations [J].
Cermak, Jan ;
Kisela, Tomas .
NONLINEAR DYNAMICS, 2015, 80 (04) :1673-1684
[9]   ASYMPTOTIC STABILITY OF DYNAMIC EQUATIONS WITH TWO FRACTIONAL TERMS: CONTINUOUS VERSUS DISCRETE CASE [J].
Cermak, Jan ;
Kisela, Tomas .
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2015, 18 (02) :437-458
[10]   Analysis of fractional differential equations with multi-orders [J].
Deng, Weihua ;
Li, Changpin ;
Guo, Qian .
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2007, 15 (02) :173-182
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