Lyapunov stability theorems for ?-Caputo derivative systems

被引：0

作者：

Lenka, Bichitra Kumar ^{[1
]}

Bora, Swaroop Nandan ^{[1
]}

机构：

[1] Indian Inst Technol Guwahati, Dept Math, Gauhati 781039, Assam, India

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2023年 / 26卷 / 01期

关键词：

Fractional calculus; -Caputo derivative; -Caputo derivative systems; Lyapunov direct method; Lyapunov stability; Lyapunov function; Asymptotic stability; ASYMPTOTIC STABILITY;

D O I：

10.1007/s13540-022-00114-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the stability concepts for psi-Caputo derivative systems in the sense of Lyapunov's idea. Two new Lyapunov theorems are formulated for the stability analysis of such systems. Many new inequalities that involve psi-Caputo derivative are developed for the application of the proposed Lyapunov theorems. Examples are provided and it is shown that the proposed theorems are very useful for predicting the limiting behavior of the trajectory of such systems starting from any initial condition imposed at any initial time on the real axis.

引用

页码：220 / 236

页数：17

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