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

页数：23

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