Nonlocal controllability of fractional measure evolution equation

In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is...

Full description

Saved in:
Bibliographic Details
Published inJournal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 18
Main Authors Gu, Haibo, Sun, Yu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.03.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Controllability
Evolution
Evolution equation
Existence theorems
Fixed points (mathematics)
Fractional calculus
Mathematics
Mathematics and Statistics
Measure of noncompactness
Mild solution
Nonlocal controllability
Evolution equation
Mild solution
Nonlocal controllability
Measure of noncompactness
Fractional calculus
Online AccessGet full text

Cover

Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
AbstractList In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . $$ \textstyle\begin{cases} {}^{C} D_{0+}^{\alpha }x(t)=Ax(t)\,dt+ (f(t,x(t))+Bu(t) )\,dg(t), \quad t\in (0, b],\\ x(0)+p(x)=x_{0}. \end{cases} $$ The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: $$ \textstyle\begin{cases} {}^{C} D_{0+}^{\alpha }x(t)=Ax(t)\,dt+ (f(t,x(t))+Bu(t) )\,dg(t), \quad t\in (0, b],\\ x(0)+p(x)=x_{0}. \end{cases} $$ { D 0 + α C x ( t ) = A x ( t ) d t + ( f ( t , x ( t ) ) + B u ( t ) ) d g ( t ) , t ∈ ( 0 , b ] , x ( 0 ) + p ( x ) = x 0 . The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: {D0+αCx(t)=Ax(t)dt+(f(t,x(t))+Bu(t))dg(t),t∈(0,b],x(0)+p(x)=x0. The regulated proposition of fractional equation is obtained for the first time. By noncompact measure method and fixed point theorems, we obtain some sufficient conditions to ensure the existence and nonlocal controllability of mild solutions. Finally, an illustrative example is given to show practical usefulness of the analytical results.
ArticleNumber 60
Author Sun, Yu
Gu, Haibo
Author_xml – sequence: 1
  givenname: Haibo
  surname: Gu
  fullname: Gu, Haibo
  email: hbgu_math@163.com
  organization: School of Mathematics Sciences, Xinjiang Normal University
– sequence: 2
  givenname: Yu
  surname: Sun
  fullname: Sun, Yu
  organization: School of Statistics and Data Sciences, Xinjiang University of Finance and Economics
BookMark eNp9UMtOwzAQtBBItIUf4BSJc8CvxM6xqnhUquACEjfLdtZVqjRu7QSpf4_bIODEYbWvmVntTNF55ztA6IbgO0JkeR8JK0ucY3oMRmVenqEJwbTKKacf53_qSzSNcYMxJUzyCZq_-K71VreZ9V0ffNtq07RNf8i8y1zQtm98l7Zb0HEIkMGnb4fjLIP9oI_FFbpwuo1w_Z1n6P3x4W3xnK9en5aL-Sq3TBZ9XhgrrTGVJYWzxnIhOQbpHMEOjGaOCg1YVFbWFogmVNZFAWVNKRbGgLBshpajbu31Ru1Cs9XhoLxu1Gngw1rp0De2BVVwoBV3jnLMObO8MqkXBDPHccGqOmndjlq74PcDxF5t_BDSn1FRJgrBCS9JQtERZYOPMYD7uUqwOtquRttVsl2dbFdlIrGRFBO4W0P4lf6H9QVV6ofg
CitedBy_id crossref_primary_10_11948_20220435
crossref_primary_10_1016_j_rinam_2024_100437
crossref_primary_10_1007_s00025_021_01507_1
crossref_primary_10_1155_2021_6615025
crossref_primary_10_11948_20230327
crossref_primary_10_3390_math10152557
crossref_primary_10_3390_math11194069
crossref_primary_10_1007_s13540_022_00075_7
Cites_doi 10.1016/S0960-0779(01)00208-9
10.1007/s00466-018-1663-9
10.1016/j.na.2007.08.042
10.1090/S0002-9939-1972-0291600-3
10.1140/epjst/e2018-00030-6
10.1016/j.jde.2003.12.002
10.1186/s13663-015-0392-4
10.1016/j.cnsns.2018.09.004
10.1007/s11071-018-4367-y
10.1186/s13662-018-1866-6
10.1016/j.jde.2011.11.005
10.1016/j.jfranklin.2018.03.012
10.1186/s13661-016-0539-1
10.1016/j.jmaa.2003.09.069
10.1016/j.sysconle.2011.09.014
10.1016/j.chaos.2005.11.062
10.1186/s13662-018-1684-x
10.1016/j.na.2006.11.018
10.1007/BFb0067476
10.1142/9069
10.1088/1751-8113/44/25/255203
10.1016/0362-546X(83)90006-8
10.1126/science.1086911
10.1016/j.nonrwa.2010.05.029
10.1007/s40096-015-0150-0
10.1016/S0034-4877(07)80100-5
10.1109/MCS.2008.931718
10.1142/3779
10.1090/trans2/010/13
ContentType Journal Article
Copyright The Author(s) 2020
Journal of Inequalities and Applications is a copyright of Springer, (2020). All Rights Reserved. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: The Author(s) 2020
– notice: Journal of Inequalities and Applications is a copyright of Springer, (2020). All Rights Reserved. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID C6C
AAYXX
CITATION
7TB
8FD
8FE
8FG
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
M7S
P5Z
P62
PIMPY
PQEST
PQQKQ
PQUKI
PTHSS
DOA
DOI 10.1186/s13660-020-02328-6
DatabaseName SpringerOpen
CrossRef
Mechanical & Transportation Engineering Abstracts
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Engineering Database
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
Publicly Available Content Database
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
Engineering Collection
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central
ProQuest Engineering Collection
ProQuest Central Korea
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
Engineering Database
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
DatabaseTitleList

CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: C6C
  name: SpringerOpen
  url: http://www.springeropen.com/
  sourceTypes: Publisher
– sequence: 2
  dbid: DOA
  name: Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 3
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Mathematics
EISSN 1029-242X
EndPage 18
ExternalDocumentID oai_doaj_org_article_54e294ff240443c49be297103f40539d
10_1186_s13660_020_02328_6
GrantInformation_xml – fundername: Scientific Research Programs of Colleges in Xinjiang
  grantid: XJEDU2018Y033
– fundername: National Natural Science Foundation of China
  grantid: 11961069
  funderid: http://dx.doi.org/10.13039/501100001809
– fundername: Natural Science Foundation of Xinjiang
  grantid: 2019D01A71; 2018D01A27
– fundername: Mathematics Key Subject of Xinjiang Normal University
  grantid: 17SDKD1106
GroupedDBID -A0
0R~
29K
2WC
4.4
40G
5GY
5VS
8FE
8FG
8R4
8R5
AAFWJ
AAJSJ
AAKKN
AAYZJ
ABDBF
ABFTD
ABJCF
ABPTK
ACACY
ACGFO
ACGFS
ACIPV
ACIWK
ADBBV
ADINQ
AENEX
AFGXO
AFKRA
AFNRJ
AFPKN
AHBXF
AHBYD
AHYZX
AIAGR
ALMA_UNASSIGNED_HOLDINGS
AMKLP
AMTXH
ARAPS
BCNDV
BENPR
BGLVJ
C24
C6C
CCPQU
CS3
D-I
DU5
EBS
ESX
GROUPED_DOAJ
HCIFZ
J9A
K6V
K7-
KQ8
L6V
M7S
M~E
OK1
P2P
P62
PIMPY
PROAC
PTHSS
Q2X
REM
RHU
RNS
RSV
SMT
SOJ
TUS
U2A
~8M
AAYXX
ABEEZ
ACULB
CITATION
EBLON
7TB
8FD
ABUWG
AZQEC
DWQXO
FR3
GNUQQ
JQ2
KR7
PQEST
PQQKQ
PQUKI
ID FETCH-LOGICAL-c385t-5bc8cbb9c15fcbc47840e8ff10feba3f27ae079c8dce1a128d55e6d2207bbe7c3
IEDL.DBID 8FG
ISSN 1029-242X
1025-5834
IngestDate Thu Jul 04 21:06:21 EDT 2024
Fri Sep 13 06:55:19 EDT 2024
Fri Aug 23 00:44:11 EDT 2024
Sat Dec 16 12:02:02 EST 2023
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Keywords Evolution equation
Mild solution
Nonlocal controllability
Measure of noncompactness
Fractional calculus
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c385t-5bc8cbb9c15fcbc47840e8ff10feba3f27ae079c8dce1a128d55e6d2207bbe7c3
OpenAccessLink https://www.proquest.com/docview/2375741461/abstract/?pq-origsite=%requestingapplication%
PQID 2375741461
PQPubID 237789
PageCount 18
ParticipantIDs doaj_primary_oai_doaj_org_article_54e294ff240443c49be297103f40539d
proquest_journals_2375741461
crossref_primary_10_1186_s13660_020_02328_6
springer_journals_10_1186_s13660_020_02328_6
PublicationCentury 2000
PublicationDate 2020-03-10
PublicationDateYYYYMMDD 2020-03-10
PublicationDate_xml – month: 03
  year: 2020
  text: 2020-03-10
  day: 10
PublicationDecade 2020
PublicationPlace Cham
PublicationPlace_xml – name: Cham
– name: Heidelberg
PublicationTitle Journal of inequalities and applications
PublicationTitleAbbrev J Inequal Appl
PublicationYear 2020
Publisher Springer International Publishing
Springer Nature B.V
SpringerOpen
Publisher_xml – name: Springer International Publishing
– name: Springer Nature B.V
– name: SpringerOpen
References Eidelman, Kochubei (CR11) 2004; 199
Federson, Mesquita, Slavik (CR7) 2012; 252
Yan, Li (CR14) 2007; 32
Zhou (CR31) 2014
Jajarmi, Hajipour, Mohammadzadeh, Baleanu (CR25) 2018; 355
Hajipour, Jajarmi, Baleanu, Sun (CR23) 2019; 69
Cao, Sun (CR6) 2016; 2016
Banas̀, Goebel (CR37) 1980
Mahmudov, Dauer (CR33) 2004; 290
Gu, Zhou, Ahmad, Alsaedi (CR22) 2017; 145
Mallik, Baleanu, Suganya, Mallika Arjunan (CR12) 2019; 27
Mahmudov (CR32) 2008; 68
Heinz (CR38) 1983; 7
Krasnoselskii (CR39) 1958; 10
Meng, Yin, Drapaca (CR28) 2019; 64
Kalamani, Baleanu, Mallika Arjunan (CR26) 2018; 1
Satco (CR8) 2014; 13
Pandit, Deo (CR2) 1982
Chen, Baleanu, Wu (CR10) 2017; 226
Zhou, Jiao (CR40) 2010; 11
Petrusel, Satco (CR5) 2015; 2015
Anguraj, Kanjanadevi, Baleanu (CR9) 2018; 24
Kronig, Penney (CR4) 1931; 130
Wan, Sun (CR35) 2012; 61
Goebel, Sanfelice, Teel (CR3) 2009; 29
Sandev, Metzler, Tomovski (CR30) 2011; 44
Yang, Luo, Karnchanaphanurach, Louie, Rech, Cova, Xun, Xie (CR15) 2003; 302
Cao, Tong, Huang (CR19) 2015; 9
Hilfer (CR24) 2000
Baleanu, Jajarmi, Asad (CR18) 2019; 71
CR20
Sivasankari, Leelamani, Baleanu, Mallika Arjunan (CR13) 2018; 12
Lakshmikantham, Vatsala (CR27) 2008; 69
Sakthivel, Mahmudov, Kim (CR34) 2007; 60
Sharma (CR1) 1972; 32
Podlubny (CR29) 1999
Baleanu, Jajarmi, Hajipour (CR16) 2018; 94
Baleanu, Jajarmi, Bonyah, Hajipour (CR17) 2018; 1
El-Borai (CR21) 2002; 14
Cao, Sun (CR36) 2017; 299
J.P. Yan (2328_CR14) 2007; 32
M. Federson (2328_CR7) 2012; 252
D. Baleanu (2328_CR17) 2018; 1
M.A. Krasnoselskii (2328_CR39) 1958; 10
A. Anguraj (2328_CR9) 2018; 24
I. Podlubny (2328_CR29) 1999
R. Kronig (2328_CR4) 1931; 130
R.R. Sharma (2328_CR1) 1972; 32
N.I. Mahmudov (2328_CR32) 2008; 68
X. Wan (2328_CR35) 2012; 61
R. Goebel (2328_CR3) 2009; 29
J. Banas̀ (2328_CR37) 1980
R. Meng (2328_CR28) 2019; 64
Y. Zhou (2328_CR31) 2014
A. Petrusel (2328_CR5) 2015; 2015
R. Sakthivel (2328_CR34) 2007; 60
D. Baleanu (2328_CR18) 2019; 71
Y.J. Cao (2328_CR36) 2017; 299
H. Yang (2328_CR15) 2003; 302
Y. Zhou (2328_CR40) 2010; 11
S.D. Eidelman (2328_CR11) 2004; 199
J.F. Cao (2328_CR19) 2015; 9
D. Mallik (2328_CR12) 2019; 27
M.M. El-Borai (2328_CR21) 2002; 14
S.G. Pandit (2328_CR2) 1982
A. Sivasankari (2328_CR13) 2018; 12
B. Satco (2328_CR8) 2014; 13
V. Lakshmikantham (2328_CR27) 2008; 69
D. Baleanu (2328_CR16) 2018; 94
H.P. Heinz (2328_CR38) 1983; 7
F. Chen (2328_CR10) 2017; 226
R. Hilfer (2328_CR24) 2000
A. Jajarmi (2328_CR25) 2018; 355
N.I. Mahmudov (2328_CR33) 2004; 290
Y.J. Cao (2328_CR6) 2016; 2016
H.B. Gu (2328_CR22) 2017; 145
P. Kalamani (2328_CR26) 2018; 1
2328_CR20
M. Hajipour (2328_CR23) 2019; 69
T. Sandev (2328_CR30) 2011; 44
References_xml – volume: 13
  start-page: 22
  year: 2014
  end-page: 31
  ident: CR8
  article-title: Regulated solutions for nonlinear measure driven equations
  publication-title: Nonlinear Anal.
  contributor:
    fullname: Satco
– volume: 14
  start-page: 433
  year: 2002
  end-page: 440
  ident: CR21
  article-title: Some probability densities and fundamental solutions of fractional evolution equations
  publication-title: Chaos Solitons Fractals
  doi: 10.1016/S0960-0779(01)00208-9
  contributor:
    fullname: El-Borai
– volume: 64
  start-page: 163
  year: 2019
  end-page: 171
  ident: CR28
  article-title: Variable-order fractional description of compression deformation of amorphous glassy polymers
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-018-1663-9
  contributor:
    fullname: Drapaca
– volume: 69
  start-page: 2677
  year: 2008
  end-page: 2682
  ident: CR27
  article-title: Basic theory of fractional differential equations
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2007.08.042
  contributor:
    fullname: Vatsala
– volume: 130
  start-page: 499
  year: 1931
  end-page: 513
  ident: CR4
  article-title: Quantum mechanics in crystal lattices
  publication-title: Proc. R. Soc. Lond.
  contributor:
    fullname: Penney
– volume: 12
  start-page: 75
  year: 2018
  end-page: 88
  ident: CR13
  article-title: Existence results for impulsive fractional neutral integro-differential equations with nonlocal conditions
  publication-title: Appl. Math.
  contributor:
    fullname: Mallika Arjunan
– volume: 32
  start-page: 503
  year: 1972
  end-page: 510
  ident: CR1
  article-title: An abstract measure differential equation
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1972-0291600-3
  contributor:
    fullname: Sharma
– volume: 226
  start-page: 3411
  year: 2017
  end-page: 3425
  ident: CR10
  article-title: Existence results of fractional differential equations with Riesz–Caputo derivative
  publication-title: Eur. Phys. J. Spec. Top.
  doi: 10.1140/epjst/e2018-00030-6
  contributor:
    fullname: Wu
– volume: 145
  year: 2017
  ident: CR22
  article-title: Integral solution of fractional evolution equations with nondense domain
  publication-title: Electron. J. Differ. Equ.
  contributor:
    fullname: Alsaedi
– volume: 199
  start-page: 211
  year: 2004
  end-page: 255
  ident: CR11
  article-title: Cauchy problem for fractional diffusion equations
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2003.12.002
  contributor:
    fullname: Kochubei
– volume: 2015
  year: 2015
  ident: CR5
  article-title: Semilinear evolution equations with distributed measures
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-015-0392-4
  contributor:
    fullname: Satco
– volume: 69
  start-page: 119
  year: 2019
  end-page: 133
  ident: CR23
  article-title: On an accurate discretization of a variable-order fractional reaction-diffusion equation
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2018.09.004
  contributor:
    fullname: Sun
– volume: 94
  start-page: 397
  year: 2018
  end-page: 414
  ident: CR16
  article-title: On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag Leffler kernel
  publication-title: Nonlinear Dyn.
  doi: 10.1007/s11071-018-4367-y
  contributor:
    fullname: Hajipour
– volume: 1
  year: 2018
  ident: CR26
  article-title: Local existence for an impulsive fractional neutral integro-differential system with Riemann–Liouville fractional derivatives in a Banach space
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-018-1866-6
  contributor:
    fullname: Mallika Arjunan
– volume: 252
  start-page: 3816
  year: 2012
  end-page: 3847
  ident: CR7
  article-title: Measure functional differential equations and functional dynamic equations on time scales
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2011.11.005
  contributor:
    fullname: Slavik
– volume: 355
  start-page: 3938
  year: 2018
  end-page: 3967
  ident: CR25
  article-title: A new approach for the nonlinear fractional optimal control problems with external persistent disturbances
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2018.03.012
  contributor:
    fullname: Baleanu
– volume: 10
  start-page: 345
  year: 1958
  end-page: 409
  ident: CR39
  article-title: Some problems of nonlinear analysis
  publication-title: Transl. Am. Math. Soc.
  contributor:
    fullname: Krasnoselskii
– volume: 2016
  year: 2016
  ident: CR6
  article-title: Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations
  publication-title: Bound. Value Probl.
  doi: 10.1186/s13661-016-0539-1
  contributor:
    fullname: Sun
– volume: 71
  start-page: 103
  issue: 1
  year: 2019
  ident: CR18
  article-title: Classical and fractional aspects of two coupled pendulums
  publication-title: Rom. Rep. Phys.
  contributor:
    fullname: Asad
– volume: 290
  start-page: 373
  year: 2004
  end-page: 394
  ident: CR33
  article-title: Controllability of stochastic semilinear functional differential systems in Hilbert space
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2003.09.069
  contributor:
    fullname: Dauer
– volume: 61
  start-page: 50
  year: 2012
  end-page: 54
  ident: CR35
  article-title: Approximate controllability for abstract measure differential systems
  publication-title: Syst. Control Lett.
  doi: 10.1016/j.sysconle.2011.09.014
  contributor:
    fullname: Sun
– volume: 32
  start-page: 725
  year: 2007
  end-page: 735
  ident: CR14
  article-title: On chaos synchronization of fractional differential equations
  publication-title: Chaos Solitons Fractals
  doi: 10.1016/j.chaos.2005.11.062
  contributor:
    fullname: Li
– year: 1980
  ident: CR37
  publication-title: Measure of Noncompactness in Banach Space
  contributor:
    fullname: Goebel
– volume: 27
  start-page: 107
  year: 2019
  end-page: 124
  ident: CR12
  article-title: Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators
  publication-title: An. Ştiinţ. Univ. ‘Ovidius’ Constanţa, Ser. Mat.
  contributor:
    fullname: Mallika Arjunan
– volume: 1
  year: 2018
  ident: CR17
  article-title: New aspects of poor nutrition in the life cycle within the fractional calculus
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-018-1684-x
  contributor:
    fullname: Hajipour
– volume: 68
  start-page: 536
  year: 2008
  end-page: 546
  ident: CR32
  article-title: Approximate controllability of evolution systems with nonlocal conditions
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2006.11.018
  contributor:
    fullname: Mahmudov
– volume: 299
  start-page: 119
  year: 2017
  end-page: 126
  ident: CR36
  article-title: Controllability of measure driven evolution systems with nonlocal conditions
  publication-title: Appl. Math. Comput.
  contributor:
    fullname: Sun
– year: 1982
  ident: CR2
  publication-title: Differential Systems Involving Impulses
  doi: 10.1007/BFb0067476
  contributor:
    fullname: Deo
– volume: 24
  start-page: 1232
  issue: 7
  year: 2018
  end-page: 1244
  ident: CR9
  article-title: On mild solution of abstract neutral fractional order impulsive differential equations with infinite delay
  publication-title: J. Comput. Anal. Appl.
  contributor:
    fullname: Baleanu
– year: 1999
  ident: CR29
  publication-title: Fractional Differential Equations
  contributor:
    fullname: Podlubny
– year: 2014
  ident: CR31
  publication-title: Basic Theory of Fractional Differential Equations
  doi: 10.1142/9069
  contributor:
    fullname: Zhou
– volume: 44
  year: 2011
  ident: CR30
  article-title: Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative
  publication-title: J. Phys. A, Math. Theor.
  doi: 10.1088/1751-8113/44/25/255203
  contributor:
    fullname: Tomovski
– volume: 7
  start-page: 1351
  year: 1983
  end-page: 1371
  ident: CR38
  article-title: On the behavior of measure of noncompactness with respect to differentiation and integration of vector-valued functions
  publication-title: Nonlinear Anal.
  doi: 10.1016/0362-546X(83)90006-8
  contributor:
    fullname: Heinz
– volume: 302
  start-page: 262
  year: 2003
  end-page: 266
  ident: CR15
  article-title: Protein conformational dynamics probed by single-molecule electron transfer
  publication-title: Science
  doi: 10.1126/science.1086911
  contributor:
    fullname: Xie
– volume: 11
  start-page: 4465
  year: 2010
  end-page: 4475
  ident: CR40
  article-title: Nonlocal Cauchy problem for fractional evolution equations
  publication-title: Nonlinear Anal., Real World Appl.
  doi: 10.1016/j.nonrwa.2010.05.029
  contributor:
    fullname: Jiao
– volume: 9
  start-page: 59
  issue: 2
  year: 2015
  end-page: 69
  ident: CR19
  article-title: Nonlocal fractional functional differential equations with measure of noncompactness in Banach space
  publication-title: Math. Sci.
  doi: 10.1007/s40096-015-0150-0
  contributor:
    fullname: Huang
– volume: 60
  start-page: 85
  year: 2007
  end-page: 96
  ident: CR34
  article-title: Approximate controllability of nonlinear impulsive differential systems
  publication-title: Rep. Math. Phys.
  doi: 10.1016/S0034-4877(07)80100-5
  contributor:
    fullname: Kim
– volume: 29
  start-page: 28
  year: 2009
  end-page: 93
  ident: CR3
  article-title: Hybrid dynamical systems
  publication-title: IEEE Control Syst. Mag.
  doi: 10.1109/MCS.2008.931718
  contributor:
    fullname: Teel
– ident: CR20
– year: 2000
  ident: CR24
  publication-title: Applications of Fractional Calculus in Physics
  doi: 10.1142/3779
  contributor:
    fullname: Hilfer
– volume: 130
  start-page: 499
  year: 1931
  ident: 2328_CR4
  publication-title: Proc. R. Soc. Lond.
  contributor:
    fullname: R. Kronig
– volume: 2016
  year: 2016
  ident: 2328_CR6
  publication-title: Bound. Value Probl.
  doi: 10.1186/s13661-016-0539-1
  contributor:
    fullname: Y.J. Cao
– volume: 27
  start-page: 107
  year: 2019
  ident: 2328_CR12
  publication-title: An. Ştiinţ. Univ. ‘Ovidius’ Constanţa, Ser. Mat.
  contributor:
    fullname: D. Mallik
– volume: 60
  start-page: 85
  year: 2007
  ident: 2328_CR34
  publication-title: Rep. Math. Phys.
  doi: 10.1016/S0034-4877(07)80100-5
  contributor:
    fullname: R. Sakthivel
– volume: 32
  start-page: 725
  year: 2007
  ident: 2328_CR14
  publication-title: Chaos Solitons Fractals
  doi: 10.1016/j.chaos.2005.11.062
  contributor:
    fullname: J.P. Yan
– volume-title: Measure of Noncompactness in Banach Space
  year: 1980
  ident: 2328_CR37
  contributor:
    fullname: J. Banas̀
– volume: 355
  start-page: 3938
  year: 2018
  ident: 2328_CR25
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2018.03.012
  contributor:
    fullname: A. Jajarmi
– volume: 12
  start-page: 75
  year: 2018
  ident: 2328_CR13
  publication-title: Appl. Math.
  contributor:
    fullname: A. Sivasankari
– volume-title: Fractional Differential Equations
  year: 1999
  ident: 2328_CR29
  contributor:
    fullname: I. Podlubny
– volume: 1
  year: 2018
  ident: 2328_CR17
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-018-1684-x
  contributor:
    fullname: D. Baleanu
– volume: 61
  start-page: 50
  year: 2012
  ident: 2328_CR35
  publication-title: Syst. Control Lett.
  doi: 10.1016/j.sysconle.2011.09.014
  contributor:
    fullname: X. Wan
– volume: 302
  start-page: 262
  year: 2003
  ident: 2328_CR15
  publication-title: Science
  doi: 10.1126/science.1086911
  contributor:
    fullname: H. Yang
– volume: 14
  start-page: 433
  year: 2002
  ident: 2328_CR21
  publication-title: Chaos Solitons Fractals
  doi: 10.1016/S0960-0779(01)00208-9
  contributor:
    fullname: M.M. El-Borai
– volume: 69
  start-page: 2677
  year: 2008
  ident: 2328_CR27
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2007.08.042
  contributor:
    fullname: V. Lakshmikantham
– volume: 32
  start-page: 503
  year: 1972
  ident: 2328_CR1
  publication-title: Proc. Am. Math. Soc.
  doi: 10.1090/S0002-9939-1972-0291600-3
  contributor:
    fullname: R.R. Sharma
– volume: 252
  start-page: 3816
  year: 2012
  ident: 2328_CR7
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2011.11.005
  contributor:
    fullname: M. Federson
– volume: 71
  start-page: 103
  issue: 1
  year: 2019
  ident: 2328_CR18
  publication-title: Rom. Rep. Phys.
  contributor:
    fullname: D. Baleanu
– volume: 290
  start-page: 373
  year: 2004
  ident: 2328_CR33
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2003.09.069
  contributor:
    fullname: N.I. Mahmudov
– ident: 2328_CR20
– volume: 2015
  year: 2015
  ident: 2328_CR5
  publication-title: Fixed Point Theory Appl.
  doi: 10.1186/s13663-015-0392-4
  contributor:
    fullname: A. Petrusel
– volume: 299
  start-page: 119
  year: 2017
  ident: 2328_CR36
  publication-title: Appl. Math. Comput.
  contributor:
    fullname: Y.J. Cao
– volume: 69
  start-page: 119
  year: 2019
  ident: 2328_CR23
  publication-title: Commun. Nonlinear Sci. Numer. Simul.
  doi: 10.1016/j.cnsns.2018.09.004
  contributor:
    fullname: M. Hajipour
– volume: 9
  start-page: 59
  issue: 2
  year: 2015
  ident: 2328_CR19
  publication-title: Math. Sci.
  doi: 10.1007/s40096-015-0150-0
  contributor:
    fullname: J.F. Cao
– volume: 11
  start-page: 4465
  year: 2010
  ident: 2328_CR40
  publication-title: Nonlinear Anal., Real World Appl.
  doi: 10.1016/j.nonrwa.2010.05.029
  contributor:
    fullname: Y. Zhou
– volume: 44
  year: 2011
  ident: 2328_CR30
  publication-title: J. Phys. A, Math. Theor.
  doi: 10.1088/1751-8113/44/25/255203
  contributor:
    fullname: T. Sandev
– volume: 145
  year: 2017
  ident: 2328_CR22
  publication-title: Electron. J. Differ. Equ.
  contributor:
    fullname: H.B. Gu
– volume: 7
  start-page: 1351
  year: 1983
  ident: 2328_CR38
  publication-title: Nonlinear Anal.
  doi: 10.1016/0362-546X(83)90006-8
  contributor:
    fullname: H.P. Heinz
– volume: 94
  start-page: 397
  year: 2018
  ident: 2328_CR16
  publication-title: Nonlinear Dyn.
  doi: 10.1007/s11071-018-4367-y
  contributor:
    fullname: D. Baleanu
– volume: 13
  start-page: 22
  year: 2014
  ident: 2328_CR8
  publication-title: Nonlinear Anal.
  contributor:
    fullname: B. Satco
– volume: 226
  start-page: 3411
  year: 2017
  ident: 2328_CR10
  publication-title: Eur. Phys. J. Spec. Top.
  doi: 10.1140/epjst/e2018-00030-6
  contributor:
    fullname: F. Chen
– volume-title: Basic Theory of Fractional Differential Equations
  year: 2014
  ident: 2328_CR31
  doi: 10.1142/9069
  contributor:
    fullname: Y. Zhou
– volume: 68
  start-page: 536
  year: 2008
  ident: 2328_CR32
  publication-title: Nonlinear Anal.
  doi: 10.1016/j.na.2006.11.018
  contributor:
    fullname: N.I. Mahmudov
– volume: 24
  start-page: 1232
  issue: 7
  year: 2018
  ident: 2328_CR9
  publication-title: J. Comput. Anal. Appl.
  contributor:
    fullname: A. Anguraj
– volume-title: Applications of Fractional Calculus in Physics
  year: 2000
  ident: 2328_CR24
  doi: 10.1142/3779
  contributor:
    fullname: R. Hilfer
– volume: 29
  start-page: 28
  year: 2009
  ident: 2328_CR3
  publication-title: IEEE Control Syst. Mag.
  doi: 10.1109/MCS.2008.931718
  contributor:
    fullname: R. Goebel
– volume: 199
  start-page: 211
  year: 2004
  ident: 2328_CR11
  publication-title: J. Differ. Equ.
  doi: 10.1016/j.jde.2003.12.002
  contributor:
    fullname: S.D. Eidelman
– volume-title: Differential Systems Involving Impulses
  year: 1982
  ident: 2328_CR2
  doi: 10.1007/BFb0067476
  contributor:
    fullname: S.G. Pandit
– volume: 1
  year: 2018
  ident: 2328_CR26
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-018-1866-6
  contributor:
    fullname: P. Kalamani
– volume: 64
  start-page: 163
  year: 2019
  ident: 2328_CR28
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-018-1663-9
  contributor:
    fullname: R. Meng
– volume: 10
  start-page: 345
  year: 1958
  ident: 2328_CR39
  publication-title: Transl. Am. Math. Soc.
  doi: 10.1090/trans2/010/13
  contributor:
    fullname: M.A. Krasnoselskii
SSID ssj0021384
ssib044744598
ssib008501289
Score 2.339496
Snippet In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x ( t ) d t...
Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: $$ \textstyle\begin{cases}...
In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions:...
Abstract In this paper, we consider the following kind of fractional evolution equation driven by measure with nonlocal conditions: { D 0 + α C x ( t ) = A x (...
SourceID doaj
proquest
crossref
springer
SourceType Open Website
Aggregation Database
Publisher
StartPage 1
SubjectTerms Analysis
Applications of Mathematics
Controllability
Evolution
Evolution equation
Existence theorems
Fixed points (mathematics)
Fractional calculus
Mathematics
Mathematics and Statistics
Measure of noncompactness
Mild solution
Nonlocal controllability
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09T8MwFLQQEwvfiEJBGdjAavwZZyyIqkKiE5W6WbFjT5BCW5D497zYDlAkxMKY2IP1nu27S57PCF0IakUFOIFBG9SYQ4axYabGzBYM-HhpSLjO534ix1N-NxOzb1d9tTVh0R44Bm4guKMl9x6Qh3NmeWngGWCReaAarKzD7ktEJ6aS1CJM8e6IjJKDJWFS5riVSoBRVGG5BkPBrX-NYv74KxrAZrSLthNLzIZxdHtowzX7aCcxxiytx-UBGk7mTUCjLJWcP0bb7fds7jO_iIcWoPUpfgnM3FuaaZl7iR7fh2g6un24GeN0KQK2TIkVFsYqa0xpifDWWF6AQnPKe5J7ZyrmaVG5vCitqq0jFaBPLYSTNaV5YYwrLDtCm828cccoE06R3LHWrJhxX8mKSgt8Q1rpSwdSsYcuuxjp5-h9oYNmUFLHiGqIqA4R1dD7ug3jZ8_Wtzq8gGzqlE39VzZ7qN8lQafFtNSUFQKID5ekh666xHw1_z6kk_8Y0inaomHitDV8fbS5Wry6MyAiK3Me5twHLqLWew
  priority: 102
  providerName: Directory of Open Access Journals
– databaseName: SpringerLink Journals (ICM)
  dbid: U2A
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELagLDDwKCDKSxnYwCLxK85YEFWF1E5U6mbFjs0CKTQFiX_PxXFaFcHAmPgiRffIfRfffUboihPDc8gTGGqDAjOwMNZUF5ialAIez3Tij_MZjcVwwh6nfLqa4_bN7u2OpP9Q-6iW4rZKqBAxrqsdSDNEYrGJtmrwULvyhPSXVVZCJWunY359bi0DeaL-NXT5Y0PU55nBPtoNADHqNxY9QBu27KK9ABajEIpVF-2MloSr1SHqj2elT0tR6D1_afi3v6KZi9y8mV6A1dfml2BkP4PLRfa9Ifs-QpPBw9P9EIfTEbChki8w10YarTOTcGe0YSmUalY6l8TO6pw6kuY2TjMjC2OTHNJQwbkVBSFxqrVNDT1GnXJW2hMUcSuT2NKatZgyl4ucCAPAQxjhMgs1Yw9dtxpTbw0JhvLFgxSq0a8C_SqvXwXSd7VSl5I1gbW_MZs_qxAPijNLMuYcAArGqGGZhmtAO9QBgqRZ0UPnrUlUiKpKEZpyQEBMJD1005pptfz3K53-T_wMbRPvMHXb3jnqLOYf9gKwx0Jfel_7BrGp0G4
  priority: 102
  providerName: Springer Nature
Title Nonlocal controllability of fractional measure evolution equation
URI https://link.springer.com/article/10.1186/s13660-020-02328-6
https://www.proquest.com/docview/2375741461/abstract/
https://doaj.org/article/54e294ff240443c49be297103f40539d
Volume 2020
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LaxsxEB7yuLSHPtKWOk3NHnprhVfP1Z6CY-KYQkwpNeQmVlqpl8ab2G4h_z4j7SMk0FwWtBLLMhppvhlpvgH4IpmTFdoJgr5BTQTOMLHc1oS7giMeLy1N5Xwul2qxEt-v5NUeLPpcmHitst8T00ZdNy7GyCeMFxKtn1B0UtkYBXC7yenNLYn1o-I5a1dMYx8OaeTEiznj84tBs7SMG_FguIUohJDlcN7AKE-1iWks7io1F316jVaTLeVK5SS6WWjfmCbqkQlLTP-P4OmTE9VkqOZv4FWHMLNpqxJvYc-vj-B1hzazbi1vj-Dl5cDYun0H02WzTnYt6y6v_2kJvO-yJmRh06Y_YO91G1PM_L9OZzN_27KFv4fV_PzXbEG68grEcS13RFqnnbWlozI460SBvp7XIdA8eFvxwIrK50XpdO08rVB8tZRe1YzlhbW-cPwDHKybtf8ImfSa5p5H2mMuQqUqphzKUjkVSo9O5wi-9hIzNy2Lhkneh1amla9B-ZokX4Ojz6JQh5GRATu9aDa_TbegjBSelSIERCRCcCdKi22ESzwgBOVlPYKTfkpMtyy35kGJRvCtn6aH7v__0vHzX_sEL1hSkHjP7wQOdpu__jOClZ0dw77IL8ZJG8dweHa-_PETWzMm4lPNxikIgM8Vm94DBqrmmQ
link.rule.ids 315,786,790,870,2115,12792,21416,27957,27958,33408,33779,40936,41154,41155,41558,42005,42223,42224,42627,43635,43840,51611,52130,52268,52269,74392,74659
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Nb9QwEB3B9gAc-CggFgrkwA2sxp9xTqhFrRborhBqpd6s2LG5wKbdbCvx7xk7TqoiwTGxFUXPY88be_wG4J1kTjboJwjGBi0ROMLEctsS7iqOfLy2NJXzWa7U4kx8OZfnecOtz2mV45qYFuq2c3GPfJ_xSqL3E4p-vLgksWpUPF3NJTTuwo7gGKrMYOfwaPXt-2RRWsYFeHLYQlRCyHo6Z2CUp5rENBZ1lZqL8VqNVvs95UqVJIZX6NeYJuqW60oK_7do6V8nqclBHT-Gh5lZFgeDKTyBO369C48yyyzyHO534cFyUmrtn8LBqlsnf1bkpPWfg3D376ILRdgM1x6w9dewl1j462yrhb8cVMKfwdnx0emnBcllFYjjWm6JtE47a2tHZXDWiQqB8zoEWgZvGx5Y1fiyqp1unacNwtdK6VXLWFlZ6yvHn8Ns3a39Cyik17T0PModcxEa1TDlEEvlVKg9BptzeD8iZi4G9QyTog6tzICvQXxNwtdg78MI6tQzKl-nF93mh8kTyUjhWS1CQCYiBHeitviMNIkHpJ68buewNw6JydOxNzfGM4cP4zDdNP_7l17-_2tv4d7idHliTj6vvr6C-ywZS8z124PZdnPlXyNh2do32Sr_AIHc4UI
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwEB6VVkJwgFJALPSRAzewNn7GOaEC3ZZHVxyo1JsVOzYX2LSbBYl_z9hxUhUJjomtKPo89nxjj78BeCmZkw36CYKxQUsEjjCx3LaEu4ojH68tTeV8zpfq7EJ8vJSXOf-pz2mV45qYFuq2c3GPfM54JdH7CUXnIadFfHm_eHN1TWIFqXjSmstp3IGdSLJjNQO9OJ1sS8u4FE-uW4hKCFlPJw6M8lSdmMbyrlJzMV6w0WreU65USWKghR6OaaJuObGk9X-LoP51pppc1WIXHmSOWRwPRvEItvxqDx5mvlnk2dzvwf3zSbO1fwzHy26VPFuR09e_DxLev4suFGE9XIDA1h_DrmLhf2WrLfz1oBf-BC4WJ1_fnZFcYIE4ruWGSOu0s7Z2VAZnnagw2vM6BFoGbxseWNX4sqqdbp2nDcLXSulVy1hZWesrx5_C9qpb-WdQSK9p6XkUPuYiNKphyiGWyqlQeww7Z_BqRMxcDToaJsUfWpkBX4P4moSvwd5vI6hTz6iBnV50628mTykjhWe1CAE5iRDcidriMxImHpCE8rqdwf44JCZPzN7cmNEMXo_DdNP87196_v-vHcFdNEfz-cPy0wu4x5KtxKS_fdjerH_6A2QuG3uYTPIPfWvkEQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Nonlocal+controllability+of+fractional+measure+evolution+equation&rft.jtitle=Journal+of+inequalities+and+applications&rft.au=Gu+Haibo&rft.au=Sun%2C+Yu&rft.date=2020-03-10&rft.pub=Springer+Nature+B.V&rft.issn=1025-5834&rft.eissn=1029-242X&rft.volume=2020&rft.issue=1&rft_id=info:doi/10.1186%2Fs13660-020-02328-6&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1029-242X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1029-242X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1029-242X&client=summon