Stability with Initial Time Difference of Caputo Fractional Differential Equations by Lyapunov Functions

被引：13

作者：

Agarwal, Ravi ^{[1
]}

O'Regan, Donal ^{[2
]}

Hristova, Snezhana ^{[3
]}

机构：

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

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

[3] Paisij Hilendarski Univ Plovdiv, Dept Appl Math & Modeling, Plovdiv 4000, Bulgaria

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2017年 / 36卷 / 01期

关键词：

Stability; Caputo derivative; Lyapunov functions; fractional differential equations; CRITERIA;

D O I：

10.4171/ZAA/1579

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The stability with initial data difference for nonlinear nonautonomous Caputo fractional differential equation is introduced. This type of stability generalizes the concept of stability in the literature and it enables us to compare the behavior of two solutions when both the initial times and initial values are different. Our theory is based on a new definition of the derivative of a Lyapunov like function along the given fractional equation. Comparison results for scalar fractional differential equations are presented and sufficient conditions for stability, uniform stability and asymptotic stability with initial time difference are obtained.

引用

页码：49 / 77

页数：29

共 33 条

[1]

Agarwal R., 2015, ELECTRON J DIFFER EQ, V49, P1

[2] Stability of Caputo fractional differential equations by Lyapunov functions [J].