Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions

被引：3

作者：

Agarwal, Ravi P. ^{[1
]}

O'Regan, Donal ^{[2
]}

Hristova, Snezhana ^{[3
]}

机构：

[1] Texas A&M Univ Kingsville, 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, Plovdiv, Bulgaria

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2017年 / 24卷 / 01期

关键词：

Strict stability; strict practical stability; different initial data; Lyapunov functions; Caputo fractional differential equations; Caputo fractional Dini derivative;

D O I：

10.1515/gmj-2016-0080

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The strict stability properties are generalized to nonlinear Caputo fractional differential equations in the case when both initial points and initial times are changeable. Using Lyapunov functions, some criteria for strict stability, eventually strict stability and strict practical stability are obtained. A brief overview of different types of derivatives in the literature related to the application of Lyapunov functions to Caputo fractional equations are given, and their advantages and disadvantages are discussed with several examples. The Caputo fractional Dini derivative with respect to to initial time difference is used to obtain some sufficient conditions.

引用

页码：1 / 13

页数：13

共 50 条

[21] Stability and boundedness of differential equations relative to initial time difference by employing vector Lyapunov functions
Wu, Zikai
Li, An
APPLIED MATHEMATICS AND COMPUTATION, 2013, 225 : 358 - 365
[22] STABILITY WITH RESPECT TO INITIAL TIME DIFFERENCE FOR GENERALIZED DELAY DIFFERENTIAL EQUATIONS
Agarwal, Ravi
Hristova, Snezhana
O'Regan, Donal
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[23] Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference
Cicek, Muhammed
Yakar, Coskun
Ogur, Bulent
SCIENTIFIC WORLD JOURNAL, 2014,
[24] Stability with respect to part of the variables of nonlinear Caputo fractional differential equations
Ben Makhlouf, Abdellatif
MATHEMATICAL COMMUNICATIONS, 2018, 23 (01) : 119 - 126
[25] Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations
Fahad, Hafiz Muhammad
Fernandez, Arran
APPLIED MATHEMATICS AND COMPUTATION, 2021, 409
[26] Generalization of practical stability for delay differential equations with respect to initial time difference
Hristova, Snezhana
39TH INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE13), 2013, 1570 : 313 - 320
[27] Some stability properties for impulsive differential equations with respect to initial time difference
Hristova, S. G.
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES (ICNPAA 2012), 2012, 1493 : 499 - 505
[28] Perturbing Lyapunov functions and stability criteria for initial time difference
McRae, FA
APPLIED MATHEMATICS AND COMPUTATION, 2001, 117 (2-3) : 313 - 320
[29] Stability of nonlinear Caputo fractional differential equations
Liu, Kewei
Jiang, Wei
APPLIED MATHEMATICAL MODELLING, 2016, 40 (5-6) : 3919 - 3924
[30] A Novel Lyapunov Asymptotic Eventual Stability Approach for Nonlinear Impulsive Caputo Fractional Differential Equations
Ante, Jackson E.
Ineh, Michael P.
Achuobi, Jonas O.
Akai, Uwem P.
Atsu, Jeremiah U.
Offiong, Nnanake-Abasi O.
APPLIEDMATH, 2024, 4 (04): : 1600 - 1617

← 1 2 3 4 5 →