Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions

Ravi Agarwal; S. Hristova; D. O'Regan

doi:10.1016/j.jfranklin.2017.02.002

Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions

Ravi Agarwal
, S. Hristova
, D. 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

41 Citations (Scopus)

Abstract

Practical stability of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. We present a new definition of the derivative of a Lyapunov like function along the given fractional differential equation with noninstantaneous impulses. Sufficient conditions for practical stability, practical quasi stability and strongly practical stability are established and several examples are given to illustrate the results.

Original language	English
Pages (from-to)	3097-3119
Number of pages	23
Journal	Journal of the Franklin Institute
Volume	354
Issue number	7
DOIs	https://doi.org/10.1016/j.jfranklin.2017.02.002
Publication status	Published - 1 May 2017

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10.1016/j.jfranklin.2017.02.002

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title = "Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions",

abstract = "Practical stability of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. We present a new definition of the derivative of a Lyapunov like function along the given fractional differential equation with noninstantaneous impulses. Sufficient conditions for practical stability, practical quasi stability and strongly practical stability are established and several examples are given to illustrate the results.",

author = "Ravi Agarwal and S. Hristova and D. O'Regan",

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AU - Agarwal, Ravi

AU - Hristova, S.

AU - O'Regan, D.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Practical stability of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. We present a new definition of the derivative of a Lyapunov like function along the given fractional differential equation with noninstantaneous impulses. Sufficient conditions for practical stability, practical quasi stability and strongly practical stability are established and several examples are given to illustrate the results.

AB - Practical stability of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. We present a new definition of the derivative of a Lyapunov like function along the given fractional differential equation with noninstantaneous impulses. Sufficient conditions for practical stability, practical quasi stability and strongly practical stability are established and several examples are given to illustrate the results.

UR - https://www.scopus.com/pages/publications/85014197290

U2 - 10.1016/j.jfranklin.2017.02.002

DO - 10.1016/j.jfranklin.2017.02.002

M3 - Article

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SP - 3097

EP - 3119

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 7

ER -

Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions

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