The Oscillation of a Class of the Fractional-Order Delay Differential Equations

The Oscillation of a Class of the Fractional-Order Delay Differential Equations

Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equ...

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Main Authors: Qianli Lu, Feng Cen
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/272198
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spelling doaj-18d1b0bb9a53495b95ea4fa23b2019ef2020-11-25T01:08:14ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/272198272198The Oscillation of a Class of the Fractional-Order Delay Differential EquationsQianli Lu0Feng Cen1Department of Control Science and Engineering, Tongji University, Shanghai 200092, ChinaDepartment of Control Science and Engineering, Tongji University, Shanghai 200092, ChinaSeveral oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.http://dx.doi.org/10.1155/2014/272198
collection DOAJ
language English
format Article
sources DOAJ
author Qianli Lu
Feng Cen
spellingShingle Qianli Lu
Feng Cen
The Oscillation of a Class of the Fractional-Order Delay Differential Equations
Discrete Dynamics in Nature and Society
author_facet Qianli Lu
Feng Cen
author_sort Qianli Lu
title The Oscillation of a Class of the Fractional-Order Delay Differential Equations
title_short The Oscillation of a Class of the Fractional-Order Delay Differential Equations
title_full The Oscillation of a Class of the Fractional-Order Delay Differential Equations
title_fullStr The Oscillation of a Class of the Fractional-Order Delay Differential Equations
title_full_unstemmed The Oscillation of a Class of the Fractional-Order Delay Differential Equations
title_sort oscillation of a class of the fractional-order delay differential equations
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2014-01-01
description Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.
url http://dx.doi.org/10.1155/2014/272198
work_keys_str_mv AT qianlilu theoscillationofaclassofthefractionalorderdelaydifferentialequations
AT fengcen theoscillationofaclassofthefractionalorderdelaydifferentialequations
AT qianlilu oscillationofaclassofthefractionalorderdelaydifferentialequations
AT fengcen oscillationofaclassofthefractionalorderdelaydifferentialequations
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