Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness

Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness

Herein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi>...

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Main Authors: Zainab Alsheekhhussain, Ahmed Gamal Ibrahim
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Symmetry
Subjects:
controllability problem
fractional differential inclusions
non-instantaneous impulsive
mild solutions
Online Access:https://www.mdpi.com/2073-8994/13/4/566
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spelling doaj-f869155b601c48c7a74730ee2790d6712021-03-29T23:02:07ZengMDPI AGSymmetry2073-89942021-03-011356656610.3390/sym13040566Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without CompactnessZainab Alsheekhhussain0Ahmed Gamal Ibrahim1Department of Mathematics, College of Sciences, University of Ha’il, Hail 55476, Saudi ArabiaDepartment of Mathematics, College of Sciences, King Faisal University, 400, Al-Ahsa 31982, Saudi ArabiaHerein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, where the linear part is a strongly continuous cosine family without compactness. We did not assume any compactness conditions on either the semi-group, the multi-valued function, or the inverse of the controllability operator, which is different from the previous literature.https://www.mdpi.com/2073-8994/13/4/566controllability problemfractional differential inclusionsnon-instantaneous impulsivemild solutions
collection DOAJ
language English
format Article
sources DOAJ
author Zainab Alsheekhhussain
Ahmed Gamal Ibrahim
spellingShingle Zainab Alsheekhhussain
Ahmed Gamal Ibrahim
Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
Symmetry
controllability problem
fractional differential inclusions
non-instantaneous impulsive
mild solutions
author_facet Zainab Alsheekhhussain
Ahmed Gamal Ibrahim
author_sort Zainab Alsheekhhussain
title Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
title_short Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
title_full Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
title_fullStr Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
title_full_unstemmed Controllability of Semilinear Multi-Valued Differential Equations with Non-Instantaneous Impulses of Order <i>α</i>∈(1,2) without Compactness
title_sort controllability of semilinear multi-valued differential equations with non-instantaneous impulses of order <i>α</i>∈(1,2) without compactness
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-03-01
description Herein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, where the linear part is a strongly continuous cosine family without compactness. We did not assume any compactness conditions on either the semi-group, the multi-valued function, or the inverse of the controllability operator, which is different from the previous literature.
topic controllability problem
fractional differential inclusions
non-instantaneous impulsive
mild solutions
url https://www.mdpi.com/2073-8994/13/4/566
work_keys_str_mv AT zainabalsheekhhussain controllabilityofsemilinearmultivalueddifferentialequationswithnoninstantaneousimpulsesoforderiai12withoutcompactness
AT ahmedgamalibrahim controllabilityofsemilinearmultivalueddifferentialequationswithnoninstantaneousimpulsesoforderiai12withoutcompactness
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