Practical stability with respect to initial time difference for Caputo fractional differential equations

被引：30

作者：

Agarwal, Ravi ^{[1
,3
]}

O'Regan, D. ^{[2
]}

Hristova, S. ^{[4
]}

Cicek, M. ^{[5
]}

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] King Abdulaziz Univ, NAAM Res Grp, Jeddah, Saudi Arabia

[4] Paisij Hilendarski Univ Plovdiv, Dept Appl Math, Plovdiv, Bulgaria

[5] Gebze Tech Univ, TR-41400 Cayirova Gebze, Turkey

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2017年 / 42卷

关键词：

Practical stability; Different initial data; Lyapunov functions; Caputo fractional differential equations; Caputo fractional Dini derivative; LYAPUNOV FUNCTIONS; DYNAMICS;

D O I：

10.1016/j.cnsns.2016.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Practical stability with initial data difference for nonlinear Caputo fractional differential equations is studied. This type of stability generalizes known concepts of stability in the literature. It enables us to compare the behavior of two solutions when both initial values and initial intervals are different. In this paper the concept of practical stability with initial time difference is generalized to Caputo fractional differential equations. A definition of the derivative of Lyapunov like function along the given nonlinear Caputo fractional differential equation is given. Comparison results using this definition and scalar fractional differential equations are proved. Sufficient conditions for several types of practical stability with initial time difference for nonlinear Caputo fractional differential equations are obtained via Lyapunov functions. Some examples are given to illustrate the results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：106 / 120

页数：15

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