Stability of Caputo fractional differential equations by Lyapunov functions

被引：81

作者：

Agarwal, Ravi ^{[1
,2
]}

O'Regan, Donal ^{[2
,3
]}

Hristova, Snezhana ^{[4
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] King Abdulaziz Univ, NAAM Res Grp, Jeddah 21589, Saudi Arabia

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

[4] Paisij Hilendarski Univ Plovdiv, Plovdiv, Bulgaria

来源：

APPLICATIONS OF MATHEMATICS | 2015年 / 60卷 / 06期

关键词：

stability; Caputo derivative; Lyapunov function; fractional differential equation;

D O I：

10.1007/s10492-015-0116-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based on the new definition of the derivative of Lyapunov functions and the new comparison result, are established.

引用

页码：653 / 676

页数：24

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