Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations

Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations

Some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worth mentioning that when α=1 the initial value problem Dαyteβt=ft,yteβt,  t∈t0,∞,  t0⩾0,  0<α<1,  yt=ϕt,  t0-h⩽t⩽t0, reduces to a classical dissipative differenti...

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Main Authors: Yajing Li, Yejuan Wang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/532589
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spelling doaj-baf5be599d5545fe9a87b789ae6fdfbd2020-11-24T23:10:16ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/532589532589Uniform Asymptotic Stability of Solutions of Fractional Functional Differential EquationsYajing Li0Yejuan Wang1School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaSome global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worth mentioning that when α=1 the initial value problem Dαyteβt=ft,yteβt,  t∈t0,∞,  t0⩾0,  0<α<1,  yt=ϕt,  t0-h⩽t⩽t0, reduces to a classical dissipative differential equation with delays as in Caraballo et al.'s work (2005).http://dx.doi.org/10.1155/2013/532589
collection DOAJ
language English
format Article
sources DOAJ
author Yajing Li
Yejuan Wang
spellingShingle Yajing Li
Yejuan Wang
Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
Abstract and Applied Analysis
author_facet Yajing Li
Yejuan Wang
author_sort Yajing Li
title Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
title_short Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
title_full Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
title_fullStr Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
title_full_unstemmed Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
title_sort uniform asymptotic stability of solutions of fractional functional differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description Some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worth mentioning that when α=1 the initial value problem Dαyteβt=ft,yteβt,  t∈t0,∞,  t0⩾0,  0<α<1,  yt=ϕt,  t0-h⩽t⩽t0, reduces to a classical dissipative differential equation with delays as in Caraballo et al.'s work (2005).
url http://dx.doi.org/10.1155/2013/532589
work_keys_str_mv AT yajingli uniformasymptoticstabilityofsolutionsoffractionalfunctionaldifferentialequations
AT yejuanwang uniformasymptoticstabilityofsolutionsoffractionalfunctionaldifferentialequations
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