Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compa...

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Main Authors: JinRong Wang, Ahmed G. Ibrahim
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2013/518306
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spelling doaj-f993e39a5b694fb7b953cf79295a44df2020-11-24T22:53:45ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/518306518306Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach SpacesJinRong Wang0Ahmed G. Ibrahim1School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, ChinaDepartment of Mathematical, Faculty of Science, King Faisal University, Al-Ahsa 31982, Saudi ArabiaWe firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.http://dx.doi.org/10.1155/2013/518306
collection DOAJ
language English
format Article
sources DOAJ
author JinRong Wang
Ahmed G. Ibrahim
spellingShingle JinRong Wang
Ahmed G. Ibrahim
Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
Journal of Function Spaces and Applications
author_facet JinRong Wang
Ahmed G. Ibrahim
author_sort JinRong Wang
title Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
title_short Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
title_full Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
title_fullStr Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
title_full_unstemmed Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces
title_sort existence and controllability results for nonlocal fractional impulsive differential inclusions in banach spaces
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
1758-4965
publishDate 2013-01-01
description We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.
url http://dx.doi.org/10.1155/2013/518306
work_keys_str_mv AT jinrongwang existenceandcontrollabilityresultsfornonlocalfractionalimpulsivedifferentialinclusionsinbanachspaces
AT ahmedgibrahim existenceandcontrollabilityresultsfornonlocalfractionalimpulsivedifferentialinclusionsinbanachspaces
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