Lyapunov Direct Method for Nonlinear Hadamard-Type Fractional Order Systems

被引：3
|
作者：
Dai, Changping [1 ]
Ma, Weiyuan [1 ]
机构：
[1] Northwest Minzu Univ, Sch Math & Comp Sci, Lanzhou 730000, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 08期
关键词：
Hadamard derivative; Caputo-Hadamard derivative; inequalities; Lyapunov direct method; asymptotical stability; STABILITY ANALYSIS; ASYMPTOTICAL STABILITY; LAW;
D O I：
10.3390/fractalfract6080405
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a rigorous Lyapunov direct method (LDM) is proposed to analyze the stability of fractional non-linear systems involving Hadamard or Caputo-Hadamard derivatives. Based on the characteristics of Hadamard-type calculus, several new inequalities are derived for different definitions. By means of the developed inequalities and modified Laplace transform, the sufficient conditions can be derived to guarantee the Hadamard-Mittag-Leffler (HML) stability of the systems. Lastly, two illustrative examples are given to show the effectiveness of our proposed results.
引用
收藏
页数：23
相关论文
共 50 条
  • [41] Some Generalized Formulas of Hadamard-Type Fractional Integral Inequalities
    Zhang, Xiujun
    Farid, Ghulam
    Yasmeen, Hafsa
    Nonlaopon, Kamsing
    JOURNAL OF FUNCTION SPACES, 2022, 2022
  • [42] On Boundedness of Fractional Hadamard Integration and Hadamard-Type Integration in Lebesgue Spaces with Mixed Norm
    Yakhshiboyev M.U.
    Journal of Mathematical Sciences, 2024, 278 (4) : 722 - 733
  • [43] Lyapunov Stability Theory for Nonlinear Nabla Fractional Order Systems
    Wei, Yiheng
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2021, 68 (10) : 3246 - 3250
  • [44] Lyapunov Function Method for Linear Fractional Order Systems
    Zhao Yige
    Wang Yuzhen
    Liu Zhi
    2015 34TH CHINESE CONTROL CONFERENCE (CCC), 2015, : 1457 - 1461
  • [45] A NOTE ON THE LYAPUNOV STABILITY OF FRACTIONAL-ORDER NONLINEAR SYSTEMS
    Dadras, Sara
    Dadras, Soodeh
    Malek, Hadi
    Chen, YangQuan
    PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2017, VOL 9, 2017,
  • [46] Lyapunov method for nonlinear fractional differential systems with delay
    Wen, Yanhua
    Zhou, Xian-Feng
    Zhang, Zhixin
    Liu, Song
    NONLINEAR DYNAMICS, 2015, 82 (1-2) : 1015 - 1025
  • [47] Lyapunov method for nonlinear fractional differential systems with delay
    Yanhua Wen
    Xian-Feng Zhou
    Zhixin Zhang
    Song Liu
    Nonlinear Dynamics, 2015, 82 : 1015 - 1025
  • [48] New results for higher-order Hadamard-type fractional differential equations on the half-line
    Senlik Cerdik, Tugba
    Yoruk Deren, Fulya
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (04) : 2315 - 2330
  • [49] Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
    Butzer, PL
    Kilbas, AA
    Trujillo, JJ
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (01) : 1 - 15
  • [50] Mathematical Analysis of the Hadamard-Type Fractional Fokker-Planck Equation
    Wang, Zhen
    Sun, Luhan
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (05)
12345