An extension of beta function, its statistical distribution, and associated fractional operator

Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summat...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Advances in difference equations Ročník 2020; číslo 1; s. 1 - 17
Hlavní autoři:	Chandola, Ankita, Mishra Pandey, Rupakshi, Agarwal, Ritu, Dutt Purohit, Sunil
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 04.12.2020 Springer Nature B.V SpringerOpen
Témata:	Analysis Appell series Applications Difference and Functional Equations Distribution functions Extended beta function Extended confluent hypergeometric function Extended hypergeometric function Functional Analysis Hypergeometric functions Integrals Lauricella function Mathematics Mathematics and Statistics Methods Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Probability distribution Representations Statistical distribution Topics in Special Functions and q-Special Functions: Theory Extended beta function Extended confluent hypergeometric function Statistical distribution Riemann–Liouville fractional operator Extended hypergeometric function Lauricella function Appell series
ISSN:	1687-1847, 1687-1839, 1687-1847
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function.
AbstractList	Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function. Abstract Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another expansion of beta function using Appell series and Lauricella function and examine various properties like integral representation and summation formula. Statistical distribution for the above extension of beta function has been defined, and the mean, variance, moment generating function and cumulative distribution function have been obtained. Using the newly defined extension of beta function, we build up the extension of hypergeometric and confluent hypergeometric functions and discuss their integral representations and differentiation formulas. Further, we define a new extension of Riemann–Liouville fractional operator using Appell series and Lauricella function and derive its various properties using the new extension of beta function.
ArticleNumber	684
Author	Mishra Pandey, Rupakshi Dutt Purohit, Sunil Chandola, Ankita Agarwal, Ritu
Author_xml	– sequence: 1 givenname: Ankita surname: Chandola fullname: Chandola, Ankita organization: Amity Institute of Applied Sciences, Amity University – sequence: 2 givenname: Rupakshi surname: Mishra Pandey fullname: Mishra Pandey, Rupakshi email: rmpandey@amity.edu organization: Amity Institute of Applied Sciences, Amity University – sequence: 3 givenname: Ritu surname: Agarwal fullname: Agarwal, Ritu organization: Malaviya National Institute of Technology – sequence: 4 givenname: Sunil surname: Dutt Purohit fullname: Dutt Purohit, Sunil organization: Rajasthan Technical University
BookMark	eNp9kU1rVTEQhoNUsK3-AVcH3Hpsvk4-lqVoLRS60XWYnExKLtfkmuSC_nvTexTFRVcZZt5neCfvBTnLJSMhbxn9wJhRV40JpfhMOZ2pYJLP6gU5Z8romRmpz_6pX5GL1naUciuNOSfuOk_4o2NuqeSpxMljhyke89pH4_2Ueptah55aTyvspzCKmvxxm0IOE7RW1gQdwxQrnLChKwes0Et9TV5G2Dd88_u9JF8_ffxy83m-f7i9u7m-n1fJbZ_BLgqiRI42CIraWxF90D4MlzRSHrgFtSi1YBTco1ho9CZ4XLRedeAgLsndtjcU2LlDTd-g_nQFkjs1Sn10UMcJe3TSSq6oWQR4kIuyBqVgGlB6vfJo5dj1btt1qOX7EVt3u3Ks46rmuNRCcKUsHyqzqdZaWqsY3ZqePqrkXiHtHaPuKRq3ReNGNO4UjVMD5f-hfww_C4kNakOcH7H-dfUM9QtXAKPm
CitedBy_id	crossref_primary_10_1142_S2661335223500090 crossref_primary_10_5269_bspm_63031 crossref_primary_10_32604_cmes_2022_016924 crossref_primary_10_3390_math12172709 crossref_primary_10_1515_anly_2021_1032
Cites_doi	10.1016/S0304-0208(06)80001-0 10.1016/j.amc.2003.09.017 10.1016/S0377-0427(96)00102-1 10.3389/fphy.2018.00079 10.5831/HMJ.2014.36.2.357 10.1002/mma.3986 10.2298/FIL1701125S 10.18576/amis/120113
ContentType	Journal Article
Copyright	The Author(s) 2020 The Author(s) 2020. 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: The Author(s) 2020. 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 3V. 7SC 7TB 7XB 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M7S P5Z P62 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U DOA
DOI	10.1186/s13662-020-03142-6
DatabaseName	Springer Nature OA Free Journals (WRLC) CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni Edition) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central ProQuest 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 Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database (ProQuest) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic DOAJ Directory of Open Access Journals
DatabaseTitle	CrossRef Publicly Available Content Database Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Central Basic ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni)
DatabaseTitleList	CrossRef Publicly Available Content Database
Database_xml	– sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics
EISSN	1687-1847
EndPage	17
ExternalDocumentID	oai_doaj_org_article_494260853aba45698e4317ae4b7c2f94 10_1186_s13662_020_03142_6
GroupedDBID	-A0 23M 2WC 3V. 4.4 40G 5GY 5VS 6J9 8FE 8FG 8R4 8R5 AAFWJ AAYZJ ABDBF ABJCF ABUWG ACGFO ACGFS ACIPV ACIWK ACUHS ADBBV ADINQ AEGXH AENEX AFKRA AFPKN AHBYD AHYZX AIAGR ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH ARAPS AZQEC BAPOH BCNDV BENPR BGLVJ BPHCQ C24 C6C CCPQU CS3 DWQXO EBS ESX GNUQQ GROUPED_DOAJ HCIFZ J9A K6V K7- KQ8 L6V M0N M7S M~E OK1 P2P P62 PIMPY PQQKQ PROAC PTHSS Q2X REM RHU RNS RSV SMT SOJ TUS U2A UPT ~8M AAYXX CITATION OVT 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D PHGZM PHGZT PKEHL PQEST PQGLB PQUKI PRINS PUEGO Q9U
ID	FETCH-LOGICAL-c429t-a956af4e2e9d30e7b93fbd7bd9480f02d29a65665ef32be350fb8dbe577c7d2a3
IEDL.DBID	DOA
ISICitedReferencesCount	9
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000596390500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1687-1847 1687-1839
IngestDate	Tue Oct 14 19:08:31 EDT 2025 Tue Sep 30 18:43:28 EDT 2025 Tue Nov 18 21:41:36 EST 2025 Sat Nov 29 01:43:49 EST 2025 Fri Feb 21 02:36:09 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Extended beta function Extended confluent hypergeometric function Statistical distribution Riemann–Liouville fractional operator Extended hypergeometric function Lauricella function Appell series
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c429t-a956af4e2e9d30e7b93fbd7bd9480f02d29a65665ef32be350fb8dbe577c7d2a3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
OpenAccessLink	https://doaj.org/article/494260853aba45698e4317ae4b7c2f94
PQID	2473326692
PQPubID	237355
PageCount	17
ParticipantIDs	doaj_primary_oai_doaj_org_article_494260853aba45698e4317ae4b7c2f94 proquest_journals_2473326692 crossref_citationtrail_10_1186_s13662_020_03142_6 crossref_primary_10_1186_s13662_020_03142_6 springer_journals_10_1186_s13662_020_03142_6
PublicationCentury	2000
PublicationDate	2020-12-04
PublicationDateYYYYMMDD	2020-12-04
PublicationDate_xml	– month: 12 year: 2020 text: 2020-12-04 day: 04
PublicationDecade	2020
PublicationPlace	Cham
PublicationPlace_xml	– name: Cham – name: New York
PublicationTitle	Advances in difference equations
PublicationTitleAbbrev	Adv Differ Equ
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	MubeenS.RahmanG.NisarK.S.ChoiJ.ArshadM.An extended beta function and its propertiesFar East J. Math. Sci.201710215451557 PuchetaP.I.An new extended beta functionInt. J. Math. Appl.201753-C255260 AgarwalR.JainS.AgarwalR.P.BaleanuD.A remark on the fractional integral operators and the image formulas of generalized Lommel–Wright functionFront. Phys.2018610.3389/fphy.2018.00079 ChoiJ.RathieA.K.ParmarR.K.Extension of extended beta, hypergeometric and confluent hypergeometric functionsHonam Math. J.2014362357385323550610.5831/HMJ.2014.36.2.357 SrivasatavaH.AgarwalR.JainS.Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributionsMath. Methods Appl. Sci.2016401255273358305110.1002/mma.3986 RainvilleE.Special Functions1971New YorkChelsea0231.33001 KilbasA.A.SrivastavaH.M.TrujilloJ.J.Theory and Applications of Fractional Differential Equations2006AmsterdamElsevier10.1016/S0304-0208(06)80001-0 ChaudhryM.A.QadirA.RafiqueM.ZubairS.Extension of Euler’s beta functionJ. Comput. Appl. Math.19977811932143677810.1016/S0377-0427(96)00102-1 GoswamiA.JainS.AgarwalP.AraciS.A note on the new extended beta and Gauss hypergeometric functionsAppl. Math. Inf. Sci.2018121139144374789110.18576/amis/120113 ChaudhryM.A.QadirA.SrivastavaH.ParisR.Extended hypergeometric and confluent hypergeometric functionsAppl. Math. Comput.2004159258960220967261067.33001 ExtonH.Multiple Hypergeometric Functions and Applications1976ChichesterEllis Horwood0337.33001 ShadabM.JabeeS.ChoiJ.An extension of beta function and its applicationFar East J. Math. Sci.20181031235251 SrivasatavaR.AgarwalR.JainS.A family of the incomplete hypergeometric functions and associated integral transforms and fractional derivative formulasFilomat2017311125140361460610.2298/FIL1701125S J. Choi (3142_CR8) 2014; 36 A. Goswami (3142_CR3) 2018; 12 P.I. Pucheta (3142_CR9) 2017; 5 R. Agarwal (3142_CR11) 2018; 6 S. Mubeen (3142_CR2) 2017; 102 M.A. Chaudhry (3142_CR7) 2004; 159 H. Exton (3142_CR4) 1976 R. Srivasatava (3142_CR13) 2017; 31 M.A. Chaudhry (3142_CR6) 1997; 78 A.A. Kilbas (3142_CR5) 2006 H. Srivasatava (3142_CR12) 2016; 40 E. Rainville (3142_CR1) 1971 M. Shadab (3142_CR10) 2018; 103
References_xml	– reference: GoswamiA.JainS.AgarwalP.AraciS.A note on the new extended beta and Gauss hypergeometric functionsAppl. Math. Inf. Sci.2018121139144374789110.18576/amis/120113 – reference: KilbasA.A.SrivastavaH.M.TrujilloJ.J.Theory and Applications of Fractional Differential Equations2006AmsterdamElsevier10.1016/S0304-0208(06)80001-0 – reference: SrivasatavaH.AgarwalR.JainS.Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributionsMath. Methods Appl. Sci.2016401255273358305110.1002/mma.3986 – reference: RainvilleE.Special Functions1971New YorkChelsea0231.33001 – reference: AgarwalR.JainS.AgarwalR.P.BaleanuD.A remark on the fractional integral operators and the image formulas of generalized Lommel–Wright functionFront. Phys.2018610.3389/fphy.2018.00079 – reference: ExtonH.Multiple Hypergeometric Functions and Applications1976ChichesterEllis Horwood0337.33001 – reference: MubeenS.RahmanG.NisarK.S.ChoiJ.ArshadM.An extended beta function and its propertiesFar East J. Math. Sci.201710215451557 – reference: ShadabM.JabeeS.ChoiJ.An extension of beta function and its applicationFar East J. Math. Sci.20181031235251 – reference: ChoiJ.RathieA.K.ParmarR.K.Extension of extended beta, hypergeometric and confluent hypergeometric functionsHonam Math. J.2014362357385323550610.5831/HMJ.2014.36.2.357 – reference: ChaudhryM.A.QadirA.RafiqueM.ZubairS.Extension of Euler’s beta functionJ. Comput. Appl. Math.19977811932143677810.1016/S0377-0427(96)00102-1 – reference: PuchetaP.I.An new extended beta functionInt. J. Math. Appl.201753-C255260 – reference: SrivasatavaR.AgarwalR.JainS.A family of the incomplete hypergeometric functions and associated integral transforms and fractional derivative formulasFilomat2017311125140361460610.2298/FIL1701125S – reference: ChaudhryM.A.QadirA.SrivastavaH.ParisR.Extended hypergeometric and confluent hypergeometric functionsAppl. Math. Comput.2004159258960220967261067.33001 – volume-title: Theory and Applications of Fractional Differential Equations year: 2006 ident: 3142_CR5 doi: 10.1016/S0304-0208(06)80001-0 – volume: 159 start-page: 589 issue: 2 year: 2004 ident: 3142_CR7 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2003.09.017 – volume: 78 start-page: 19 issue: 1 year: 1997 ident: 3142_CR6 publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(96)00102-1 – volume: 6 year: 2018 ident: 3142_CR11 publication-title: Front. Phys. doi: 10.3389/fphy.2018.00079 – volume: 36 start-page: 357 issue: 2 year: 2014 ident: 3142_CR8 publication-title: Honam Math. J. doi: 10.5831/HMJ.2014.36.2.357 – volume: 5 start-page: 255 issue: 3-C year: 2017 ident: 3142_CR9 publication-title: Int. J. Math. Appl. – volume: 40 start-page: 255 issue: 1 year: 2016 ident: 3142_CR12 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3986 – volume: 31 start-page: 125 issue: 1 year: 2017 ident: 3142_CR13 publication-title: Filomat doi: 10.2298/FIL1701125S – volume-title: Special Functions year: 1971 ident: 3142_CR1 – volume: 102 start-page: 1545 year: 2017 ident: 3142_CR2 publication-title: Far East J. Math. Sci. – volume-title: Multiple Hypergeometric Functions and Applications year: 1976 ident: 3142_CR4 – volume: 103 start-page: 235 issue: 1 year: 2018 ident: 3142_CR10 publication-title: Far East J. Math. Sci. – volume: 12 start-page: 139 issue: 1 year: 2018 ident: 3142_CR3 publication-title: Appl. Math. Inf. Sci. doi: 10.18576/amis/120113
SSID	ssj0029488
Score	2.2793946
Snippet	Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present another... Abstract Recently, various forms of extended beta function have been proposed and presented by many researchers. The principal goal of this paper is to present...
SourceID	doaj proquest crossref springer
SourceType	Open Website Aggregation Database Enrichment Source Index Database Publisher
StartPage	1
SubjectTerms	Analysis Appell series Applications Difference and Functional Equations Distribution functions Extended beta function Extended confluent hypergeometric function Extended hypergeometric function Functional Analysis Hypergeometric functions Integrals Lauricella function Mathematics Mathematics and Statistics Methods Operators (mathematics) Ordinary Differential Equations Partial Differential Equations Probability distribution Representations Statistical distribution Topics in Special Functions and q-Special Functions: Theory
SummonAdditionalLinks	– databaseName: Computer Science Database dbid: K7- link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PbxQhFH7R6kEP1p9xazUcvLmkM8DCcGqqaWNi0njQpDcCw8OYmJnt7urfXx7LbG0Te_E6A4TwPXgfD_gewHvMmGZWEXmSXlAKM8u9NZKLNqnU-k4l35RkE-b8vLu4sF9rwG1dr1VOa2JZqOPYU4z8SCgjM9XQVhwvLzlljaLT1ZpC4z48aIVoyc6_GL7bcFlV8k62Ok8kYgLTo5lOH61bqbXgtHkiAXfB9Q3HVPT7b5DOW-ekxf2c7f9vx5_Ck0o82cnWUp7BPRyew-O_5AhfgDsZWAmKUwSNjYkF3HhGno_Qm7OfmzWjB0hF2zm3FUl0t-bLmjM_ROYr2BhZWm2fTORy4xLLYf5L-H52-u3TZ14TMPA-u6lNRm2hfVIo0EbZoAlWphBNiHlgm9SIKKwnPrjAJEVAuWhS6GLAhTG9icLLV7A3jAO-BpbrZibZpV4EpVQurbXPXKLrkUJ7AWfQTqPv-qpOTkkyfrmyS-m02yLmMmKuIOb0DD7s6iy32hx3lv5IoO5Kkq52-TCufrg6TZ2ypNifKYwPPlNL2yERLI8qmF4kq2ZwOIHs6mRfu2uEZzCfzOT697-7dHB3a2_gkSADpcsz6hD2Nqvf-BYe9n8yzqt3xdSvAIL6AoU priority: 102 providerName: ProQuest
Title	An extension of beta function, its statistical distribution, and associated fractional operator
URI	https://link.springer.com/article/10.1186/s13662-020-03142-6 https://www.proquest.com/docview/2473326692 https://doaj.org/article/494260853aba45698e4317ae4b7c2f94
Volume	2020
WOSCitedRecordID	wos000596390500001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1687-1847 dateEnd: 20221231 omitProxy: false ssIdentifier: ssj0029488 issn: 1687-1847 databaseCode: DOA dateStart: 20040101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Nb9QwEB1VbQ9wQFBALLQrH3rrRs3ajh0f26oVCLGKCpVaLpYd2xISyla7C7-fGScpLVLhwiWHeBxZbyZ64683AIcRfYpZRSiScJxKmJnCGS0KPk8yzV0tkytzsQm9WNTX16a5V-qLzoT18sA9cMfSkIY6korzDsne1JEoz0XpdcuTyUqgmPWMk6lhqmUwLscrMrU6Xs-FUrygqRLJtfNCPaChrNb_IMX8Y1c0k83Fc3g2ZInspB_dC9iK3R48vacd-BLsScfyCjYtd7FlYj5uHCOaIqhn7Ntmzei2UBZixm8FUsgdilvNmOsCc4NnYmBp1d9vQLvlbcw776_g6uL8y9n7YqiWULTIKRuEuFIuycijCaKM2huRfNA-IBZlKnngxlHyVsUkuI-iKpOvg4-V1q0O3InXsN0tu_gGGPbFtK9OLfdSSrRWyiHx122kdTgfJzAfwbPtICVOFS2-2zylqJXtAbcIuM2AWzWBo7s-t72Qxl-tT8knd5Ykgp1fYGjYITTsv0JjAvujR-3wZ64tl1pgyqoMn8Bs9PLv5seH9PZ_DOkdPOEUhXQeRu7D9mb1Ix7AbvsTo2E1hZ3T80VzOc2xjM-PupjSYdTP-Gyqr9jefPjU3PwCOzj33Q
linkProvider	Directory of Open Access Journals
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VggQcylcrlhbwAU5s1KzjteNDhcpH1WrLikORejN2bCOkKll2FxB_it_YGSfZUiR664FrYltO_Dx-HnvmAbwIOKbIKnwWC8tJwkxnVqsi46Mo4siWIto8iU2o6bQ8PdUf1-B3HwtD1yp7m5gMtW8q8pHvcqEKpBpS89ezbxmpRtHpai-h0cJiEn79xC3bYu_oHY7vS84P3p-8Pcw6VYGsQtu7xK6MpY0i8KB9kQfldBGdV85rUeYx555rSyRnHGLBXSjGeXSld2GsVKU8twW2ewNuCvxGytU_Udlqg4ctpNA7iROXmEcfpFPK3cWokJJntFmjhPE8k5cWwqQXcInk_nUum5a7g3v_24-6DxsdsWb77Ux4AGuhfgh3_0i3-AjMfs2S0588hKyJzIWlZbSyEzqH7OtywSjAKuWuxrY8JRXu9MCGzNae2Q7MwbM4b0NCsFwzC-mywiZ8upYv3IL1uqnDY2BYF5lyGSvuhBBYWkqLXKmsArkuXRjAqB9tU3XZ10kE5MykXVgpTYsQgwgxCSFGDuDVqs6szT1yZek3BKJVScobnh408y-mM0NGaFIkQIpmnUXqrMtABNIG4VTFoxYD2OlBZTpjtjAXiBrAsIflxet_d-nJ1a09h9uHJx-OzfHRdLINdzhNDrooJHZgfTn_Hp7CreoHjvn8WZpmDD5fN1zPAZ9KYas
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VghAc-CxioYAPcGKjzTqOHR8QKpQV1aJVDyD1ZuzYRkgoWXYXEH-NX8eMk2wpEr31wDWxLSd-M37-mHkATwOOKbIKn8XCcpIw05nVqsj4NIo4tZWINk9iE2qxqE5O9PEO_BpiYeha5eATk6P2bU175BMuVIFUQ2o-if21iOPD2cvl14wUpOikdZDT6CAyDz9_4PJt_eLoEMf6GeezN-9fv816hYGsRj-8wW6V0kYReNC-yINyuojOK-e1qPKYc8-1JcJThlhwF4oyj67yLpRK1cpzW2C7l-AyzsIl2dhcZdvFHraQwvAkGjGxkCFgp5KT9bSQkme0cKPk8TyTZybFpB1whvD-dUabpr7Zzf_5p92CGz3hZgedhdyGndDcget_pGG8C-agYekwgHYOWRuZCxvLaMYn1I7Z582aUeBVymmNbXlKNtzrhI2ZbTyzPciDZ3HVhYpguXYZ0iWGPfhwIV94D3abtgn3gWFdZNBVrLkTQmBpKS1yqKoOtKXpwgimw8ibus_KTuIgX0xanVXSdGgxiBaT0GLkCJ5v6yy7nCTnln5FgNqWpHzi6UG7-mR692SEJqUCpG7WWaTUugpELG0QTtU8ajGC_QFgpndya3OKrhGMB4ievv53lx6c39oTuIooNe-OFvOHcI2TndD9IbEPu5vVt_AIrtTfcchXj5PFMfh40Wj9DUYlamU
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=An+extension+of+beta+function%2C+its+statistical+distribution%2C+and+associated+fractional+operator&rft.jtitle=Advances+in+difference+equations&rft.au=Ankita+Chandola&rft.au=Rupakshi+Mishra+Pandey&rft.au=Ritu+Agarwal&rft.au=Sunil+Dutt+Purohit&rft.date=2020-12-04&rft.pub=SpringerOpen&rft.eissn=1687-1847&rft.volume=2020&rft.issue=1&rft.spage=1&rft.epage=17&rft_id=info:doi/10.1186%2Fs13662-020-03142-6&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_494260853aba45698e4317ae4b7c2f94
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1687-1847&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1687-1847&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1687-1847&client=summon