SOME STABILITY PROPERTIES RELATED TO INITIAL TIME DIFFERENCE FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Ravi Agarwal; Snezhana Hristova; Donal O'Regan

doi:10.13025/28410

SOME STABILITY PROPERTIES RELATED TO INITIAL TIME DIFFERENCE FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Ravi Agarwal
, Snezhana Hristova
, Donal O'Regan

Mathematics

Texas A&M University-Kingsville
University of Plovdiv Paisii Hilendarski

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

11 Citations (Scopus)

Abstract

Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.

Original language	English (Ireland)
Pages (from-to)	72-93
Number of pages	22
Journal	FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume	21
Issue number	1
DOIs	https://doi.org/10.13025/28410 https://doi.org/10.1515/fca-2018-0005
Publication status	Published - 1 Feb 2018

Keywords

Caputo fractional differential equations
initial data difference
Lipschitz stability
Lyapunov functions
Mittag-Leffler stability

Access to Document

10.13025/28410Licence: CC BY-NC-ND
10.1515/fca-2018-0005

Cite this

@article{9f70bd4a55394cc38479890a0cecc6e5,

title = "SOME STABILITY PROPERTIES RELATED TO INITIAL TIME DIFFERENCE FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS",

abstract = "Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.",

keywords = "Caputo fractional differential equations, initial data difference, Lipschitz stability, Lyapunov functions, Mittag-Leffler stability",

author = "Ravi Agarwal and Snezhana Hristova and Donal O'Regan",

note = "Publisher Copyright: {\textcopyright} 2018 Diogenes Co., Sofia.",

year = "2018",

month = feb,

day = "1",

doi = "10.13025/28410",

language = "English (Ireland)",

volume = "21",

pages = "72--93",

journal = "FRACTIONAL CALCULUS AND APPLIED ANALYSIS",

number = "1",

}

TY - JOUR

T1 - SOME STABILITY PROPERTIES RELATED TO INITIAL TIME DIFFERENCE FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

AU - Agarwal, Ravi

AU - Hristova, Snezhana

AU - O'Regan, Donal

PY - 2018/2/1

Y1 - 2018/2/1

N2 - Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.

AB - Lipschitz stability and Mittag-Leffler stability with initial time difference for nonlinear nonautonomous Caputo fractional differential equation are defined and studied using Lyapunov like functions. Some sufficient conditions are obtained. The fractional order extension of comparison principles via scalar fractional differential equations with a parameter is employed. The relation between both types of stability is discussed theoretically and it is illustrated with examples.

KW - Caputo fractional differential equations

KW - initial data difference

KW - Lipschitz stability

KW - Lyapunov functions

KW - Mittag-Leffler stability

UR - http://hdl.handle.net/10379/10136

UR - https://www.scopus.com/pages/publications/85044280388

U2 - 10.13025/28410

DO - 10.13025/28410

M3 - Article

VL - 21

SP - 72

EP - 93

JO - FRACTIONAL CALCULUS AND APPLIED ANALYSIS

JF - FRACTIONAL CALCULUS AND APPLIED ANALYSIS

IS - 1

ER -

SOME STABILITY PROPERTIES RELATED TO INITIAL TIME DIFFERENCE FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this