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.
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页数：23
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