On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus Article Swipe

PDF

Ahmed Bakhet , Abd‐Allah Hyder , Areej A. Almoneef , Mohamed Niyaz , Ahmed H. Soliman ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.3390/math10224371

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hypergeometric matrix function and state some integral equations and differential formulas about it. Next, we obtain some results about fractional calculus of these extended incomplete Wright hypergeometric matrix functions. Finally, we discuss an application of the extended incomplete Wright hypergeometric matrix function in the kinetic equations.

Related Topics

Mathematics

Generalization

Calculus (Dental)

Mathematical Analysis

Concepts

Generalized hypergeometric function Matrix function Mathematics Wright Hypergeometric function of a matrix argument Basic hypergeometric series Matrix (chemical analysis) Generalization Extension (predicate logic) Pure mathematics Algebra over a field Hypergeometric function Calculus (dental) Mathematical analysis Symmetric matrix Computer science Physics Programming language Dentistry Medicine Quantum mechanics Composite material Materials science Eigenvalues and eigenvectors

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.3390/math10224371
PDF: https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123
OA Status: gold
Cited By: 4
References: 32
Related Works: 10
OpenAlex ID: https://openalex.org/W4309787642

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4309787642

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.3390/math10224371

Digital Object Identifier
Title: On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2022

Year of publication
Publication date: 2022-11-20

Full publication date if available
Authors: Ahmed Bakhet, Abd‐Allah Hyder, Areej A. Almoneef, Mohamed Niyaz, Ahmed H. Soliman

List of authors in order
Landing page: https://doi.org/10.3390/math10224371

Publisher landing page
PDF URL: https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: gold

Open access status per OpenAlex
OA URL: https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123

Direct OA link when available
Concepts: Generalized hypergeometric function, Matrix function, Mathematics, Wright, Hypergeometric function of a matrix argument, Basic hypergeometric series, Matrix (chemical analysis), Generalization, Extension (predicate logic), Pure mathematics, Algebra over a field, Hypergeometric function, Calculus (dental), Mathematical analysis, Symmetric matrix, Computer science, Physics, Programming language, Dentistry, Medicine, Quantum mechanics, Composite material, Materials science, Eigenvalues and eigenvectors

Top concepts (fields/topics) attached by OpenAlex
Cited by: 4

Total citation count in OpenAlex
Citations by year (recent): 2025: 2, 2024: 1, 2023: 1

Per-year citation counts (last 5 years)
References (count): 32

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4309787642
doi	https://doi.org/10.3390/math10224371
ids.doi	https://doi.org/10.3390/math10224371
ids.openalex	https://openalex.org/W4309787642
fwci	0.69736577
type	article
title	On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus
awards[0].id	https://openalex.org/G2365641567
awards[0].funder_id	https://openalex.org/F4320324433
awards[0].display_name
awards[0].funder_award_id	RGP.2/15/43
awards[0].funder_display_name	King Khalid University
biblio.issue	22
biblio.volume	10
biblio.last_page	4371
biblio.first_page	4371
topics[0].id	https://openalex.org/T10288
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9977999925613403
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2611
topics[0].subfield.display_name	Modeling and Simulation
topics[0].display_name	Fractional Differential Equations Solutions
topics[1].id	https://openalex.org/T11191
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9965999722480774
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2604
topics[1].subfield.display_name	Applied Mathematics
topics[1].display_name	Mathematical functions and polynomials
topics[2].id	https://openalex.org/T12661
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9962000250816345
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2612
topics[2].subfield.display_name	Numerical Analysis
topics[2].display_name	Iterative Methods for Nonlinear Equations
funders[0].id	https://openalex.org/F4320324433
funders[0].ror	https://ror.org/052kwzs30
funders[0].display_name	King Khalid University
is_xpac	False
apc_list.value	1800
apc_list.currency	CHF
apc_list.value_usd	1949
apc_paid.value	1800
apc_paid.currency	CHF
apc_paid.value_usd	1949
concepts[0].id	https://openalex.org/C158241908
concepts[0].level	3
concepts[0].score	0.6816580295562744
concepts[0].wikidata	https://www.wikidata.org/wiki/Q109744257
concepts[0].display_name	Generalized hypergeometric function
concepts[1].id	https://openalex.org/C4263655
concepts[1].level	4
concepts[1].score	0.6590940952301025
concepts[1].wikidata	https://www.wikidata.org/wiki/Q2699958
concepts[1].display_name	Matrix function
concepts[2].id	https://openalex.org/C33923547
concepts[2].level	0
concepts[2].score	0.6549378037452698
concepts[2].wikidata	https://www.wikidata.org/wiki/Q395
concepts[2].display_name	Mathematics
concepts[3].id	https://openalex.org/C2777667586
concepts[3].level	2
concepts[3].score	0.6461102962493896
concepts[3].wikidata	https://www.wikidata.org/wiki/Q8038170
concepts[3].display_name	Wright
concepts[4].id	https://openalex.org/C165175332
concepts[4].level	4
concepts[4].score	0.5630140900611877
concepts[4].wikidata	https://www.wikidata.org/wiki/Q5958021
concepts[4].display_name	Hypergeometric function of a matrix argument
concepts[5].id	https://openalex.org/C92941272
concepts[5].level	3
concepts[5].score	0.5429356694221497
concepts[5].wikidata	https://www.wikidata.org/wiki/Q1062958
concepts[5].display_name	Basic hypergeometric series
concepts[6].id	https://openalex.org/C106487976
concepts[6].level	2
concepts[6].score	0.49351346492767334
concepts[6].wikidata	https://www.wikidata.org/wiki/Q685816
concepts[6].display_name	Matrix (chemical analysis)
concepts[7].id	https://openalex.org/C177148314
concepts[7].level	2
concepts[7].score	0.4686203598976135
concepts[7].wikidata	https://www.wikidata.org/wiki/Q170084
concepts[7].display_name	Generalization
concepts[8].id	https://openalex.org/C2778029271
concepts[8].level	2
concepts[8].score	0.4621793329715729
concepts[8].wikidata	https://www.wikidata.org/wiki/Q5421931
concepts[8].display_name	Extension (predicate logic)
concepts[9].id	https://openalex.org/C202444582
concepts[9].level	1
concepts[9].score	0.45660120248794556
concepts[9].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[9].display_name	Pure mathematics
concepts[10].id	https://openalex.org/C136119220
concepts[10].level	2
concepts[10].score	0.42071324586868286
concepts[10].wikidata	https://www.wikidata.org/wiki/Q1000660
concepts[10].display_name	Algebra over a field
concepts[11].id	https://openalex.org/C197320386
concepts[11].level	2
concepts[11].score	0.4062209725379944
concepts[11].wikidata	https://www.wikidata.org/wiki/Q21028472
concepts[11].display_name	Hypergeometric function
concepts[12].id	https://openalex.org/C2777686260
concepts[12].level	2
concepts[12].score	0.32163310050964355
concepts[12].wikidata	https://www.wikidata.org/wiki/Q144037
concepts[12].display_name	Calculus (dental)
concepts[13].id	https://openalex.org/C134306372
concepts[13].level	1
concepts[13].score	0.28432387113571167
concepts[13].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[13].display_name	Mathematical analysis
concepts[14].id	https://openalex.org/C54848796
concepts[14].level	3
concepts[14].score	0.2062034010887146
concepts[14].wikidata	https://www.wikidata.org/wiki/Q339011
concepts[14].display_name	Symmetric matrix
concepts[15].id	https://openalex.org/C41008148
concepts[15].level	0
concepts[15].score	0.12034595012664795
concepts[15].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[15].display_name	Computer science
concepts[16].id	https://openalex.org/C121332964
concepts[16].level	0
concepts[16].score	0.08543571829795837
concepts[16].wikidata	https://www.wikidata.org/wiki/Q413
concepts[16].display_name	Physics
concepts[17].id	https://openalex.org/C199360897
concepts[17].level	1
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q9143
concepts[17].display_name	Programming language
concepts[18].id	https://openalex.org/C199343813
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q12128
concepts[18].display_name	Dentistry
concepts[19].id	https://openalex.org/C71924100
concepts[19].level	0
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q11190
concepts[19].display_name	Medicine
concepts[20].id	https://openalex.org/C62520636
concepts[20].level	1
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q944
concepts[20].display_name	Quantum mechanics
concepts[21].id	https://openalex.org/C159985019
concepts[21].level	1
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q181790
concepts[21].display_name	Composite material
concepts[22].id	https://openalex.org/C192562407
concepts[22].level	0
concepts[22].score	0.0
concepts[22].wikidata	https://www.wikidata.org/wiki/Q228736
concepts[22].display_name	Materials science
concepts[23].id	https://openalex.org/C158693339
concepts[23].level	2
concepts[23].score	0.0
concepts[23].wikidata	https://www.wikidata.org/wiki/Q190524
concepts[23].display_name	Eigenvalues and eigenvectors
keywords[0].id	https://openalex.org/keywords/generalized-hypergeometric-function
keywords[0].score	0.6816580295562744
keywords[0].display_name	Generalized hypergeometric function
keywords[1].id	https://openalex.org/keywords/matrix-function
keywords[1].score	0.6590940952301025
keywords[1].display_name	Matrix function
keywords[2].id	https://openalex.org/keywords/mathematics
keywords[2].score	0.6549378037452698
keywords[2].display_name	Mathematics
keywords[3].id	https://openalex.org/keywords/wright
keywords[3].score	0.6461102962493896
keywords[3].display_name	Wright
keywords[4].id	https://openalex.org/keywords/hypergeometric-function-of-a-matrix-argument
keywords[4].score	0.5630140900611877
keywords[4].display_name	Hypergeometric function of a matrix argument
keywords[5].id	https://openalex.org/keywords/basic-hypergeometric-series
keywords[5].score	0.5429356694221497
keywords[5].display_name	Basic hypergeometric series
keywords[6].id	https://openalex.org/keywords/matrix
keywords[6].score	0.49351346492767334
keywords[6].display_name	Matrix (chemical analysis)
keywords[7].id	https://openalex.org/keywords/generalization
keywords[7].score	0.4686203598976135
keywords[7].display_name	Generalization
keywords[8].id	https://openalex.org/keywords/extension
keywords[8].score	0.4621793329715729
keywords[8].display_name	Extension (predicate logic)
keywords[9].id	https://openalex.org/keywords/pure-mathematics
keywords[9].score	0.45660120248794556
keywords[9].display_name	Pure mathematics
keywords[10].id	https://openalex.org/keywords/algebra-over-a-field
keywords[10].score	0.42071324586868286
keywords[10].display_name	Algebra over a field
keywords[11].id	https://openalex.org/keywords/hypergeometric-function
keywords[11].score	0.4062209725379944
keywords[11].display_name	Hypergeometric function
keywords[12].id	https://openalex.org/keywords/calculus
keywords[12].score	0.32163310050964355
keywords[12].display_name	Calculus (dental)
keywords[13].id	https://openalex.org/keywords/mathematical-analysis
keywords[13].score	0.28432387113571167
keywords[13].display_name	Mathematical analysis
keywords[14].id	https://openalex.org/keywords/symmetric-matrix
keywords[14].score	0.2062034010887146
keywords[14].display_name	Symmetric matrix
keywords[15].id	https://openalex.org/keywords/computer-science
keywords[15].score	0.12034595012664795
keywords[15].display_name	Computer science
keywords[16].id	https://openalex.org/keywords/physics
keywords[16].score	0.08543571829795837
keywords[16].display_name	Physics
language	en
locations[0].id	doi:10.3390/math10224371
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4210192031
locations[0].source.issn	2227-7390
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2227-7390
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	Mathematics
locations[0].source.host_organization	https://openalex.org/P4310310987
locations[0].source.host_organization_name	Multidisciplinary Digital Publishing Institute
locations[0].source.host_organization_lineage	https://openalex.org/P4310310987
locations[0].source.host_organization_lineage_names	Multidisciplinary Digital Publishing Institute
locations[0].license	cc-by
locations[0].pdf_url	https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123
locations[0].version	publishedVersion
locations[0].raw_type	journal-article
locations[0].license_id	https://openalex.org/licenses/cc-by
locations[0].is_accepted	True
locations[0].is_published	True
locations[0].raw_source_name	Mathematics
locations[0].landing_page_url	https://doi.org/10.3390/math10224371
locations[1].id	pmh:oai:doaj.org/article:717397930ef94b55b6c666dc29d66f74
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306401280
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	False
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	DOAJ (DOAJ: Directory of Open Access Journals)
locations[1].source.host_organization
locations[1].source.host_organization_name
locations[1].license	cc-by-sa
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by-sa
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name	Mathematics, Vol 10, Iss 22, p 4371 (2022)
locations[1].landing_page_url	https://doaj.org/article/717397930ef94b55b6c666dc29d66f74
locations[2].id	pmh:oai:mdpi.com:/2227-7390/10/22/4371/
locations[2].is_oa	True
locations[2].source.id	https://openalex.org/S4306400947
locations[2].source.issn
locations[2].source.type	repository
locations[2].source.is_oa	True
locations[2].source.issn_l
locations[2].source.is_core	False
locations[2].source.is_in_doaj	False
locations[2].source.display_name	MDPI (MDPI AG)
locations[2].source.host_organization	https://openalex.org/I4210097602
locations[2].source.host_organization_name	Multidisciplinary Digital Publishing Institute (Switzerland)
locations[2].source.host_organization_lineage	https://openalex.org/I4210097602
locations[2].license	cc-by
locations[2].pdf_url
locations[2].version	submittedVersion
locations[2].raw_type	Text
locations[2].license_id	https://openalex.org/licenses/cc-by
locations[2].is_accepted	False
locations[2].is_published	False
locations[2].raw_source_name	Pages: 4371
locations[2].landing_page_url	https://dx.doi.org/10.3390/math10224371
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5046121670
authorships[0].author.orcid	https://orcid.org/0000-0001-5454-380X
authorships[0].author.display_name	Ahmed Bakhet
authorships[0].countries	EG
authorships[0].affiliations[0].institution_ids	https://openalex.org/I184834183
authorships[0].affiliations[0].raw_affiliation_string	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
authorships[0].institutions[0].id	https://openalex.org/I184834183
authorships[0].institutions[0].ror	https://ror.org/05fnp1145
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I184834183
authorships[0].institutions[0].country_code	EG
authorships[0].institutions[0].display_name	Al-Azhar University
authorships[0].author_position	first
authorships[0].raw_author_name	Ahmed Bakhet
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
authorships[1].author.id	https://openalex.org/A5048312355
authorships[1].author.orcid	https://orcid.org/0000-0001-9273-9512
authorships[1].author.display_name	Abd‐Allah Hyder
authorships[1].countries	EG, SA
authorships[1].affiliations[0].institution_ids	https://openalex.org/I82952536
authorships[1].affiliations[0].raw_affiliation_string	Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
authorships[1].affiliations[1].institution_ids	https://openalex.org/I184834183
authorships[1].affiliations[1].raw_affiliation_string	Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 11371, Egypt
authorships[1].institutions[0].id	https://openalex.org/I184834183
authorships[1].institutions[0].ror	https://ror.org/05fnp1145
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I184834183
authorships[1].institutions[0].country_code	EG
authorships[1].institutions[0].display_name	Al-Azhar University
authorships[1].institutions[1].id	https://openalex.org/I82952536
authorships[1].institutions[1].ror	https://ror.org/052kwzs30
authorships[1].institutions[1].type	education
authorships[1].institutions[1].lineage	https://openalex.org/I82952536
authorships[1].institutions[1].country_code	SA
authorships[1].institutions[1].display_name	King Khalid University
authorships[1].author_position	middle
authorships[1].raw_author_name	Abd-Allah Hyder
authorships[1].is_corresponding	False
authorships[1].raw_affiliation_strings	Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 11371, Egypt, Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
authorships[2].author.id	https://openalex.org/A5076617733
authorships[2].author.orcid	https://orcid.org/0000-0001-7041-3730
authorships[2].author.display_name	Areej A. Almoneef
authorships[2].countries	SA
authorships[2].affiliations[0].institution_ids	https://openalex.org/I106778892
authorships[2].affiliations[0].raw_affiliation_string	Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
authorships[2].institutions[0].id	https://openalex.org/I106778892
authorships[2].institutions[0].ror	https://ror.org/05b0cyh02
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I106778892
authorships[2].institutions[0].country_code	SA
authorships[2].institutions[0].display_name	Princess Nourah bint Abdulrahman University
authorships[2].author_position	middle
authorships[2].raw_author_name	Areej A. Almoneef
authorships[2].is_corresponding	True
authorships[2].raw_affiliation_strings	Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
authorships[3].author.id	https://openalex.org/A5091865417
authorships[3].author.orcid	https://orcid.org/0009-0002-2401-5330
authorships[3].author.display_name	Mohamed Niyaz
authorships[3].countries	EG
authorships[3].affiliations[0].institution_ids	https://openalex.org/I184834183
authorships[3].affiliations[0].raw_affiliation_string	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
authorships[3].institutions[0].id	https://openalex.org/I184834183
authorships[3].institutions[0].ror	https://ror.org/05fnp1145
authorships[3].institutions[0].type	education
authorships[3].institutions[0].lineage	https://openalex.org/I184834183
authorships[3].institutions[0].country_code	EG
authorships[3].institutions[0].display_name	Al-Azhar University
authorships[3].author_position	middle
authorships[3].raw_author_name	Mohamed Niyaz
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
authorships[4].author.id	https://openalex.org/A5051829976
authorships[4].author.orcid	https://orcid.org/0000-0001-5732-0847
authorships[4].author.display_name	Ahmed H. Soliman
authorships[4].countries	EG
authorships[4].affiliations[0].institution_ids	https://openalex.org/I184834183
authorships[4].affiliations[0].raw_affiliation_string	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
authorships[4].institutions[0].id	https://openalex.org/I184834183
authorships[4].institutions[0].ror	https://ror.org/05fnp1145
authorships[4].institutions[0].type	education
authorships[4].institutions[0].lineage	https://openalex.org/I184834183
authorships[4].institutions[0].country_code	EG
authorships[4].institutions[0].display_name	Al-Azhar University
authorships[4].author_position	last
authorships[4].raw_author_name	Ahmed H. Soliman
authorships[4].is_corresponding	False
authorships[4].raw_affiliation_strings	Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T10288
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9977999925613403
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2611
primary_topic.subfield.display_name	Modeling and Simulation
primary_topic.display_name	Fractional Differential Equations Solutions
related_works	https://openalex.org/W3192609840, https://openalex.org/W2047062626, https://openalex.org/W2010866598, https://openalex.org/W4306707509, https://openalex.org/W2905308183, https://openalex.org/W4289106892, https://openalex.org/W3047997887, https://openalex.org/W2325544293, https://openalex.org/W1969129728, https://openalex.org/W1557546324
cited_by_count	4
counts_by_year[0].year	2025
counts_by_year[0].cited_by_count	2
counts_by_year[1].year	2024
counts_by_year[1].cited_by_count	1
counts_by_year[2].year	2023
counts_by_year[2].cited_by_count	1
locations_count	3
best_oa_location.id	doi:10.3390/math10224371
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4210192031
best_oa_location.source.issn	2227-7390
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2227-7390
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	Mathematics
best_oa_location.source.host_organization	https://openalex.org/P4310310987
best_oa_location.source.host_organization_name	Multidisciplinary Digital Publishing Institute
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310310987
best_oa_location.source.host_organization_lineage_names	Multidisciplinary Digital Publishing Institute
best_oa_location.license	cc-by
best_oa_location.pdf_url	https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123
best_oa_location.version	publishedVersion
best_oa_location.raw_type	journal-article
best_oa_location.license_id	https://openalex.org/licenses/cc-by
best_oa_location.is_accepted	True
best_oa_location.is_published	True
best_oa_location.raw_source_name	Mathematics
best_oa_location.landing_page_url	https://doi.org/10.3390/math10224371
primary_location.id	doi:10.3390/math10224371
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4210192031
primary_location.source.issn	2227-7390
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2227-7390
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	Mathematics
primary_location.source.host_organization	https://openalex.org/P4310310987
primary_location.source.host_organization_name	Multidisciplinary Digital Publishing Institute
primary_location.source.host_organization_lineage	https://openalex.org/P4310310987
primary_location.source.host_organization_lineage_names	Multidisciplinary Digital Publishing Institute
primary_location.license	cc-by
primary_location.pdf_url	https://www.mdpi.com/2227-7390/10/22/4371/pdf?version=1669104123
primary_location.version	publishedVersion
primary_location.raw_type	journal-article
primary_location.license_id	https://openalex.org/licenses/cc-by
primary_location.is_accepted	True
primary_location.is_published	True
primary_location.raw_source_name	Mathematics
primary_location.landing_page_url	https://doi.org/10.3390/math10224371
publication_date	2022-11-20
publication_year	2022
referenced_works	https://openalex.org/W2097616588, https://openalex.org/W6667912487, https://openalex.org/W4243049761, https://openalex.org/W6799530109, https://openalex.org/W3210157435, https://openalex.org/W4256061566, https://openalex.org/W2570760802, https://openalex.org/W3028956740, https://openalex.org/W2911592480, https://openalex.org/W2123304508, https://openalex.org/W2003124459, https://openalex.org/W2036448292, https://openalex.org/W2751555766, https://openalex.org/W2401770454, https://openalex.org/W4200327197, https://openalex.org/W2899896117, https://openalex.org/W3028946846, https://openalex.org/W3011722031, https://openalex.org/W6650414922, https://openalex.org/W2091714372, https://openalex.org/W4247953052, https://openalex.org/W2948298435, https://openalex.org/W3082835985, https://openalex.org/W1966793822, https://openalex.org/W2964216698, https://openalex.org/W4282035423, https://openalex.org/W4285220996, https://openalex.org/W1261935558, https://openalex.org/W2596974018, https://openalex.org/W2071031363, https://openalex.org/W1999421818, https://openalex.org/W3186342360
referenced_works_count	32
abstract_inverted_index.a	6, 27
abstract_inverted_index.an	66
abstract_inverted_index.by	16
abstract_inverted_index.in	76
abstract_inverted_index.of	9, 29, 55, 68
abstract_inverted_index.we	3, 25, 48, 64
abstract_inverted_index.and	37, 42
abstract_inverted_index.it.	46
abstract_inverted_index.new	7
abstract_inverted_index.the	10, 18, 30, 69, 77
abstract_inverted_index.give	26
abstract_inverted_index.some	39, 50
abstract_inverted_index.this	1
abstract_inverted_index.will	4
abstract_inverted_index.Next,	47
abstract_inverted_index.about	45, 52
abstract_inverted_index.state	38
abstract_inverted_index.these	56
abstract_inverted_index.using	17
abstract_inverted_index.First,	24
abstract_inverted_index.Wright	12, 33, 59, 72
abstract_inverted_index.matrix	14, 22, 35, 61, 74
abstract_inverted_index.obtain	49
abstract_inverted_index.Through	0
abstract_inverted_index.discuss	5, 65
abstract_inverted_index.kinetic	78
abstract_inverted_index.results	51
abstract_inverted_index.symbol.	23
abstract_inverted_index.Finally,	63
abstract_inverted_index.article,	2
abstract_inverted_index.calculus	54
abstract_inverted_index.extended	19, 31, 57, 70
abstract_inverted_index.formulas	44
abstract_inverted_index.function	15, 36, 75
abstract_inverted_index.integral	40
abstract_inverted_index.equations	41
abstract_inverted_index.extension	8
abstract_inverted_index.Pochhammer	21
abstract_inverted_index.equations.	79
abstract_inverted_index.fractional	53
abstract_inverted_index.functions.	62
abstract_inverted_index.incomplete	11, 20, 32, 58, 71
abstract_inverted_index.application	67
abstract_inverted_index.differential	43
abstract_inverted_index.generalization	28
abstract_inverted_index.hypergeometric	13, 34, 60, 73
cited_by_percentile_year.max	97
cited_by_percentile_year.min	89
corresponding_author_ids	https://openalex.org/A5076617733
countries_distinct_count	2
institutions_distinct_count	5
corresponding_institution_ids	https://openalex.org/I106778892
citation_normalized_percentile.value	0.63376962
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False