On asymptotic properties of solutions to fractional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Cong, N. D.¹  Tuan, H. T.¹  Trinh, H.² 

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

[2] Deakin Univ, Sch Engn, Fac Sci Engn & Built Environm, Geelong, Vic 3217, Australia

关键词: Fractional differential equation;    Lyapunov's first method;    Lyapunov's second method;    Asymptotic behavior;    Asymptotic stability;    Mittag-Leffler stability;   

DOI  :  10.1016/j.jmaa.2019.123759

来源: Elsevier

【 摘 要 】

We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE cannot converge to the fixed points faster than t(-alpha), where alpha is the order of the FDE. Then, we introduce the notion of Mittag-Leffler stability which is suitable for systems of fractional-order. Next, we use this notion to describe the asymptotic behavior of solutions to FDEs by two approaches: Lyapunov's first method and Lyapunov's second method. Finally, we give a discussion on the relation between Lipschitz condition, stability and speed of decay, separation of trajectories to scalar FDEs. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free