Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used

The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the R...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 11318 - 11329
Main Authors SABATIER, Jocelyn, FARGES, Christophe
Format Journal Article
LanguageEnglish
Published AIMS Press 01.10.2021
Subjects
caputo definition
grünwald-letnikov definition
initial conditions
memory
riemann-liouville definition
time fractional derivative
Online AccessGet full text

Cover

Abstract The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of time fractional model analysis in which initial conditions are involved.
AbstractList The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of time fractional model analysis in which initial conditions are involved.
Author FARGES, Christophe
SABATIER, Jocelyn
Author_xml – sequence: 1
  givenname: Jocelyn
  surname: SABATIER
  fullname: SABATIER, Jocelyn
– sequence: 2
  givenname: Christophe
  surname: FARGES
  fullname: FARGES, Christophe
BookMark eNptkdtKxDAQhoMoeNo7HyAPYDWnJu2liIcFwRu9LtNkaiPdZkmyq769rS4i4tX8zPzzDcx_TPbHMCIhZ5xdyFqqyxXk_kIwwXVp9siRUEYWuq6q_V_6kCxSemVscgkljDoi78vRZw8D3cKwQbqOoR1wlWjqw2ZwdAyZtkghpWA9ZHQ0B9pFsNmHcdpaBYcDdZhs9Ou5l-hbP_m2GGnucZpEv4Xst7Ps_HwrjHST0J2Sgw6GhItdPSHPtzdP1_fFw-Pd8vrqobBCSFNoriXvuGKAQmnDGJY1YCeZ5srW2jhUEkTpurLiIGutWMklINjKcCOklCdk-c11AV6bdfQriB9NAN98NUJ8aSBmbwdsaqiqqtataplRExGMdqqUwGonbWXNxDr_ZtkYUorY_fA4a-YQmjmEZhfCZBd_7NZnmD-QI_jh_6VPcRmOlQ
CitedBy_id crossref_primary_10_1007_s12215_024_01175_4
crossref_primary_10_3390_fractalfract6100550
crossref_primary_10_3390_fractalfract8040201
crossref_primary_10_1016_j_aeue_2022_154293
crossref_primary_10_3390_fractalfract6030137
crossref_primary_10_3390_act13120534
crossref_primary_10_3390_s23167179
crossref_primary_10_3934_math_20231025
Cites_doi 10.1103/PhysRevE.102.052102
10.1016/S0165-1684(03)00183-X
10.1016/j.matcom.2021.02.021
10.3390/fractalfract4010001
10.1016/j.aej.2021.03.008
10.3390/math6020016
10.1016/j.ijmecsci.2020.105992
10.3390/sym13061099
10.1016/j.camwa.2009.08.036
10.1177/1077546313481839
10.2298/TSCI160111018A
10.1155/2011/562494
10.1016/j.cnsns.2009.05.070
10.1186/s13662-015-0739-5
10.23919/ECC.2001.7076126
10.3390/fractalfract4030036
10.1016/j.physe.2009.09.006
10.3390/math8020196
10.1007/s11071-004-3756-6
10.1006/jmaa.2000.7194
10.1016/j.apnum.2019.01.004
10.1016/j.jare.2021.04.008
10.1016/j.aml.2018.05.013
10.3390/fractalfract4030040
10.1016/j.matcom.2021.05.018
10.1080/01969722.2020.1758470
10.1155/2014/238459
10.1016/j.cam.2018.02.030
10.1098/rspa.2020.0200
10.1016/j.jare.2020.04.004
10.1002/mma.7360
ContentType Journal Article
CorporateAuthor Bordeaux University, IMS Laboratory, UMR 5218 CNRS, 351 Cours de la Libération, 33405 Talence -France
CorporateAuthor_xml – name: Bordeaux University, IMS Laboratory, UMR 5218 CNRS, 351 Cours de la Libération, 33405 Talence -France
DBID AAYXX
CITATION
DOA
DOI 10.3934/math.2021657
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2473-6988
EndPage 11329
ExternalDocumentID oai_doaj_org_article_9a88896b4b074df5a76d453a09d3c8c7
10_3934_math_2021657
GroupedDBID AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
FRJ
GROUPED_DOAJ
IAO
ITC
M~E
OK1
RAN
ID FETCH-LOGICAL-c2237-61631f140ae246700e59aef30614c967de43a25df581a39640513aeac87172333
IEDL.DBID DOA
ISSN 2473-6988
IngestDate Wed Aug 27 01:02:36 EDT 2025
Tue Jul 01 03:56:49 EDT 2025
Thu Apr 24 23:08:43 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 10
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c2237-61631f140ae246700e59aef30614c967de43a25df581a39640513aeac87172333
OpenAccessLink https://doaj.org/article/9a88896b4b074df5a76d453a09d3c8c7
PageCount 12
ParticipantIDs doaj_primary_oai_doaj_org_article_9a88896b4b074df5a76d453a09d3c8c7
crossref_primary_10_3934_math_2021657
crossref_citationtrail_10_3934_math_2021657
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 20211001
PublicationDateYYYYMMDD 2021-10-01
PublicationDate_xml – month: 10
  year: 2021
  text: 20211001
  day: 01
PublicationDecade 2020
PublicationTitle AIMS mathematics
PublicationYear 2021
Publisher AIMS Press
Publisher_xml – name: AIMS Press
References key-10.3934/math.2021657-31
key-10.3934/math.2021657-30
key-10.3934/math.2021657-19
key-10.3934/math.2021657-18
key-10.3934/math.2021657-11
key-10.3934/math.2021657-33
key-10.3934/math.2021657-10
key-10.3934/math.2021657-32
key-10.3934/math.2021657-13
key-10.3934/math.2021657-35
key-10.3934/math.2021657-12
key-10.3934/math.2021657-34
key-10.3934/math.2021657-15
key-10.3934/math.2021657-14
key-10.3934/math.2021657-36
key-10.3934/math.2021657-17
key-10.3934/math.2021657-16
key-10.3934/math.2021657-9
key-10.3934/math.2021657-20
key-10.3934/math.2021657-5
key-10.3934/math.2021657-6
key-10.3934/math.2021657-7
key-10.3934/math.2021657-8
key-10.3934/math.2021657-1
key-10.3934/math.2021657-2
key-10.3934/math.2021657-3
key-10.3934/math.2021657-4
key-10.3934/math.2021657-29
key-10.3934/math.2021657-22
key-10.3934/math.2021657-21
key-10.3934/math.2021657-24
key-10.3934/math.2021657-23
key-10.3934/math.2021657-26
key-10.3934/math.2021657-25
key-10.3934/math.2021657-28
key-10.3934/math.2021657-27
References_xml – ident: key-10.3934/math.2021657-10
– ident: key-10.3934/math.2021657-12
– ident: key-10.3934/math.2021657-24
  doi: 10.1103/PhysRevE.102.052102
– ident: key-10.3934/math.2021657-3
  doi: 10.1016/S0165-1684(03)00183-X
– ident: key-10.3934/math.2021657-34
  doi: 10.1016/j.matcom.2021.02.021
– ident: key-10.3934/math.2021657-23
  doi: 10.3390/fractalfract4010001
– ident: key-10.3934/math.2021657-35
  doi: 10.1016/j.aej.2021.03.008
– ident: key-10.3934/math.2021657-16
  doi: 10.3390/math6020016
– ident: key-10.3934/math.2021657-31
  doi: 10.1016/j.ijmecsci.2020.105992
– ident: key-10.3934/math.2021657-28
  doi: 10.3390/sym13061099
– ident: key-10.3934/math.2021657-7
  doi: 10.1016/j.camwa.2009.08.036
– ident: key-10.3934/math.2021657-27
  doi: 10.1177/1077546313481839
– ident: key-10.3934/math.2021657-19
  doi: 10.2298/TSCI160111018A
– ident: key-10.3934/math.2021657-26
– ident: key-10.3934/math.2021657-11
  doi: 10.1155/2011/562494
– ident: key-10.3934/math.2021657-6
  doi: 10.1016/j.cnsns.2009.05.070
– ident: key-10.3934/math.2021657-13
  doi: 10.1186/s13662-015-0739-5
– ident: key-10.3934/math.2021657-2
  doi: 10.23919/ECC.2001.7076126
– ident: key-10.3934/math.2021657-9
  doi: 10.3390/fractalfract4030036
– ident: key-10.3934/math.2021657-30
  doi: 10.1016/j.physe.2009.09.006
– ident: key-10.3934/math.2021657-18
  doi: 10.3390/math8020196
– ident: key-10.3934/math.2021657-4
  doi: 10.1007/s11071-004-3756-6
– ident: key-10.3934/math.2021657-14
  doi: 10.1006/jmaa.2000.7194
– ident: key-10.3934/math.2021657-15
  doi: 10.1016/j.apnum.2019.01.004
– ident: key-10.3934/math.2021657-32
  doi: 10.1016/j.jare.2021.04.008
– ident: key-10.3934/math.2021657-21
  doi: 10.1016/j.aml.2018.05.013
– ident: key-10.3934/math.2021657-1
– ident: key-10.3934/math.2021657-22
  doi: 10.3390/fractalfract4030040
– ident: key-10.3934/math.2021657-33
  doi: 10.1016/j.matcom.2021.05.018
– ident: key-10.3934/math.2021657-5
– ident: key-10.3934/math.2021657-20
  doi: 10.1080/01969722.2020.1758470
– ident: key-10.3934/math.2021657-17
  doi: 10.1155/2014/238459
– ident: key-10.3934/math.2021657-8
  doi: 10.1016/j.cam.2018.02.030
– ident: key-10.3934/math.2021657-29
  doi: 10.1098/rspa.2020.0200
– ident: key-10.3934/math.2021657-25
  doi: 10.1016/j.jare.2020.04.004
– ident: key-10.3934/math.2021657-36
  doi: 10.1002/mma.7360
SSID ssj0002124274
Score 2.1595004
Snippet The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 11318
SubjectTerms caputo definition
grünwald-letnikov definition
initial conditions
memory
riemann-liouville definition
time fractional derivative
Title Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used
URI https://doaj.org/article/9a88896b4b074df5a76d453a09d3c8c7
Volume 6
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT4QwEG7MnvRgfMb1lR70ZMgCLYUe1bhZTdaTm-yNtLTNmhjWAKv-fGcKEi7GizcCAzTTYR5h5vsIuXI6kdIVOohYYgIwCvikdCiDLIuUM6xQJsV55_mzmC340zJZDqi-sCeshQduFTeRCmo0KTTXEOyMS1QqDE-YCiU8KSv8HDnEvEExhT4YHDKHeqvtdGeS8Qnkf_jvIY4ERqJBDBpA9fuYMt0ju10ySG_bReyTLVsekJ15j6RaH5KvR-zuASFE5ba043-pab1CbmparhuqLVWdkq2hzZq6qp1WgLs80Q01tncONf1cKWQyqyi8Ba5Unt7sAw_da-kbuOimtuaILKYPL_ezoGNLCAoI8TjrJ1jkoF5SNuY4fGMTqaxjWPIVUqTGcqbiBFQI28CkgEwtYgr8LpRMacwYOyajcl3aE0K5UAaRBlWskCs91FlmZegEE4hiq-IxufnRX150UOLIaPGWQ0mB2s5R23mn7TG57qXfWwiNX-TucCt6GQS-9ifAHPLOHPK_zOH0Px5yRrZxTW3P3jkZNdXGXkDu0ehLb2bf55_Ytg
linkProvider Directory of Open Access Journals
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=Initial+value+problems+should+not+be+associated+to+fractional+model+descriptions+whatever+the+derivative+definition+used&rft.jtitle=AIMS+mathematics&rft.au=Jocelyn+SABATIER&rft.au=Christophe+FARGES&rft.date=2021-10-01&rft.pub=AIMS+Press&rft.eissn=2473-6988&rft.volume=6&rft.issue=10&rft.spage=11318&rft.epage=11329&rft_id=info:doi/10.3934%2Fmath.2021657&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_9a88896b4b074df5a76d453a09d3c8c7
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon