Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay

Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay

This paper considers the approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈ (1, 2] with finite delay. Using the contraction mapping principle, we explore the existence and uniqueness of the mild solution. Furthermore, under certain hypotheses, the...

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Main Authors: Ma Saisai, Kou Chunhai, Ge Fudong
Format: Article
Language:English
Published: Academic Journals Center of Shanghai Normal University 2017-06-01
Series:Journal of Shanghai Normal University (Natural Sciences)
Subjects:
approximate controllability
fractional evolution equation
finite delay
<i>α</i>-order cosine family
contraction mapping principle
Online Access:http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/view_abstract.aspx?file_no=20170306&flag=1
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spelling doaj-19abe7cbcf6d48c6bb68132de70ba4c62020-11-24T22:45:52ZengAcademic Journals Center of Shanghai Normal UniversityJournal of Shanghai Normal University (Natural Sciences)1000-51371000-51372017-06-0146338439210.3969/J.ISSN.100-5137.2017.03.00620170306Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delayMa Saisai0Kou Chunhai1Ge Fudong2College of Science, Donghua UniversityCollege of Science, Donghua UniversityCollege of Information Science and Technology, Donghua UniversityThis paper considers the approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈ (1, 2] with finite delay. Using the contraction mapping principle, we explore the existence and uniqueness of the mild solution. Furthermore, under certain hypotheses, the approximate controllability is obtained by the theory of strongly continuous-order cosine family. As an illustration of the application of the obtained result, an example is given at last.http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/view_abstract.aspx?file_no=20170306&flag=1approximate controllabilityfractional evolution equationfinite delay<i>α</i>-order cosine familycontraction mapping principle
collection DOAJ
language English
format Article
sources DOAJ
author Ma Saisai
Kou Chunhai
Ge Fudong
spellingShingle Ma Saisai
Kou Chunhai
Ge Fudong
Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
Journal of Shanghai Normal University (Natural Sciences)
approximate controllability
fractional evolution equation
finite delay
<i>α</i>-order cosine family
contraction mapping principle
author_facet Ma Saisai
Kou Chunhai
Ge Fudong
author_sort Ma Saisai
title Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
title_short Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
title_full Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
title_fullStr Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
title_full_unstemmed Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
title_sort approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay
publisher Academic Journals Center of Shanghai Normal University
series Journal of Shanghai Normal University (Natural Sciences)
issn 1000-5137
1000-5137
publishDate 2017-06-01
description This paper considers the approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈ (1, 2] with finite delay. Using the contraction mapping principle, we explore the existence and uniqueness of the mild solution. Furthermore, under certain hypotheses, the approximate controllability is obtained by the theory of strongly continuous-order cosine family. As an illustration of the application of the obtained result, an example is given at last.
topic approximate controllability
fractional evolution equation
finite delay
<i>α</i>-order cosine family
contraction mapping principle
url http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/view_abstract.aspx?file_no=20170306&flag=1
work_keys_str_mv AT masaisai approximatecontrollabilityofsemilinearfractionalevolutionequationsoforderiai12withfinitedelay
AT kouchunhai approximatecontrollabilityofsemilinearfractionalevolutionequationsoforderiai12withfinitedelay
AT gefudong approximatecontrollabilityofsemilinearfractionalevolutionequationsoforderiai12withfinitedelay
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