Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms Article Swipe

PDF

Ahmed M. Hassan , Osama Moaaz , Sameh Askar , Ahmad M. Alshamrani ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.3389/fams.2024.1384559

This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria.

Related Topics

Mathematics

Differential (Mechanical Device)

Differential Equation

Mathematical Analysis

Concepts

Mathematics Applied mathematics Riccati equation Order (exchange) Linear map Transformation (genetics) Operator (biology) Linear differential equation Differential (mechanical device) Type (biology) Differential equation Canonical form Mathematical analysis Pure mathematics Physics Chemistry Finance Biology Biochemistry Thermodynamics Economics Repressor Gene Ecology Transcription factor

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.3389/fams.2024.1384559
PDF: https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf
OA Status: gold
References: 26
Related Works: 10
OpenAlex ID: https://openalex.org/W4400695464

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4400695464

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.3389/fams.2024.1384559

Digital Object Identifier
Title: Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-07-16

Full publication date if available
Authors: Ahmed M. Hassan, Osama Moaaz, Sameh Askar, Ahmad M. Alshamrani

List of authors in order
Landing page: https://doi.org/10.3389/fams.2024.1384559

Publisher landing page
PDF URL: https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf

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.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf

Direct OA link when available
Concepts: Mathematics, Applied mathematics, Riccati equation, Order (exchange), Linear map, Transformation (genetics), Operator (biology), Linear differential equation, Differential (mechanical device), Type (biology), Differential equation, Canonical form, Mathematical analysis, Pure mathematics, Physics, Chemistry, Finance, Biology, Biochemistry, Thermodynamics, Economics, Repressor, Gene, Ecology, Transcription factor

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
References (count): 26

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

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4400695464
doi	https://doi.org/10.3389/fams.2024.1384559
ids.doi	https://doi.org/10.3389/fams.2024.1384559
ids.openalex	https://openalex.org/W4400695464
fwci	0.0
type	article
title	Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms
biblio.issue
biblio.volume	10
biblio.last_page
biblio.first_page
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	0.9998000264167786
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/T12727
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9997000098228455
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2612
topics[1].subfield.display_name	Numerical Analysis
topics[1].display_name	Differential Equations and Numerical Methods
topics[2].id	https://openalex.org/T10541
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9995999932289124
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2604
topics[2].subfield.display_name	Applied Mathematics
topics[2].display_name	Nonlinear Differential Equations Analysis
is_xpac	False
apc_list.value	1150
apc_list.currency	USD
apc_list.value_usd	1150
apc_paid.value	1150
apc_paid.currency	USD
apc_paid.value_usd	1150
concepts[0].id	https://openalex.org/C33923547
concepts[0].level	0
concepts[0].score	0.6295437216758728
concepts[0].wikidata	https://www.wikidata.org/wiki/Q395
concepts[0].display_name	Mathematics
concepts[1].id	https://openalex.org/C28826006
concepts[1].level	1
concepts[1].score	0.5881716012954712
concepts[1].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[1].display_name	Applied mathematics
concepts[2].id	https://openalex.org/C45473103
concepts[2].level	3
concepts[2].score	0.576113760471344
concepts[2].wikidata	https://www.wikidata.org/wiki/Q851503
concepts[2].display_name	Riccati equation
concepts[3].id	https://openalex.org/C182306322
concepts[3].level	2
concepts[3].score	0.5611971616744995
concepts[3].wikidata	https://www.wikidata.org/wiki/Q1779371
concepts[3].display_name	Order (exchange)
concepts[4].id	https://openalex.org/C49766605
concepts[4].level	2
concepts[4].score	0.5291398167610168
concepts[4].wikidata	https://www.wikidata.org/wiki/Q207643
concepts[4].display_name	Linear map
concepts[5].id	https://openalex.org/C204241405
concepts[5].level	3
concepts[5].score	0.517547070980072
concepts[5].wikidata	https://www.wikidata.org/wiki/Q461499
concepts[5].display_name	Transformation (genetics)
concepts[6].id	https://openalex.org/C17020691
concepts[6].level	5
concepts[6].score	0.5075355768203735
concepts[6].wikidata	https://www.wikidata.org/wiki/Q139677
concepts[6].display_name	Operator (biology)
concepts[7].id	https://openalex.org/C13982400
concepts[7].level	3
concepts[7].score	0.47095733880996704
concepts[7].wikidata	https://www.wikidata.org/wiki/Q1129902
concepts[7].display_name	Linear differential equation
concepts[8].id	https://openalex.org/C93226319
concepts[8].level	2
concepts[8].score	0.46367785334587097
concepts[8].wikidata	https://www.wikidata.org/wiki/Q193137
concepts[8].display_name	Differential (mechanical device)
concepts[9].id	https://openalex.org/C2777299769
concepts[9].level	2
concepts[9].score	0.4539681077003479
concepts[9].wikidata	https://www.wikidata.org/wiki/Q3707858
concepts[9].display_name	Type (biology)
concepts[10].id	https://openalex.org/C78045399
concepts[10].level	2
concepts[10].score	0.4364592432975769
concepts[10].wikidata	https://www.wikidata.org/wiki/Q11214
concepts[10].display_name	Differential equation
concepts[11].id	https://openalex.org/C204707403
concepts[11].level	2
concepts[11].score	0.42875000834465027
concepts[11].wikidata	https://www.wikidata.org/wiki/Q1152398
concepts[11].display_name	Canonical form
concepts[12].id	https://openalex.org/C134306372
concepts[12].level	1
concepts[12].score	0.27854496240615845
concepts[12].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[12].display_name	Mathematical analysis
concepts[13].id	https://openalex.org/C202444582
concepts[13].level	1
concepts[13].score	0.0875784158706665
concepts[13].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[13].display_name	Pure mathematics
concepts[14].id	https://openalex.org/C121332964
concepts[14].level	0
concepts[14].score	0.056616753339767456
concepts[14].wikidata	https://www.wikidata.org/wiki/Q413
concepts[14].display_name	Physics
concepts[15].id	https://openalex.org/C185592680
concepts[15].level	0
concepts[15].score	0.0
concepts[15].wikidata	https://www.wikidata.org/wiki/Q2329
concepts[15].display_name	Chemistry
concepts[16].id	https://openalex.org/C10138342
concepts[16].level	1
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q43015
concepts[16].display_name	Finance
concepts[17].id	https://openalex.org/C86803240
concepts[17].level	0
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q420
concepts[17].display_name	Biology
concepts[18].id	https://openalex.org/C55493867
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q7094
concepts[18].display_name	Biochemistry
concepts[19].id	https://openalex.org/C97355855
concepts[19].level	1
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q11473
concepts[19].display_name	Thermodynamics
concepts[20].id	https://openalex.org/C162324750
concepts[20].level	0
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q8134
concepts[20].display_name	Economics
concepts[21].id	https://openalex.org/C158448853
concepts[21].level	4
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q425218
concepts[21].display_name	Repressor
concepts[22].id	https://openalex.org/C104317684
concepts[22].level	2
concepts[22].score	0.0
concepts[22].wikidata	https://www.wikidata.org/wiki/Q7187
concepts[22].display_name	Gene
concepts[23].id	https://openalex.org/C18903297
concepts[23].level	1
concepts[23].score	0.0
concepts[23].wikidata	https://www.wikidata.org/wiki/Q7150
concepts[23].display_name	Ecology
concepts[24].id	https://openalex.org/C86339819
concepts[24].level	3
concepts[24].score	0.0
concepts[24].wikidata	https://www.wikidata.org/wiki/Q407384
concepts[24].display_name	Transcription factor
keywords[0].id	https://openalex.org/keywords/mathematics
keywords[0].score	0.6295437216758728
keywords[0].display_name	Mathematics
keywords[1].id	https://openalex.org/keywords/applied-mathematics
keywords[1].score	0.5881716012954712
keywords[1].display_name	Applied mathematics
keywords[2].id	https://openalex.org/keywords/riccati-equation
keywords[2].score	0.576113760471344
keywords[2].display_name	Riccati equation
keywords[3].id	https://openalex.org/keywords/order
keywords[3].score	0.5611971616744995
keywords[3].display_name	Order (exchange)
keywords[4].id	https://openalex.org/keywords/linear-map
keywords[4].score	0.5291398167610168
keywords[4].display_name	Linear map
keywords[5].id	https://openalex.org/keywords/transformation
keywords[5].score	0.517547070980072
keywords[5].display_name	Transformation (genetics)
keywords[6].id	https://openalex.org/keywords/operator
keywords[6].score	0.5075355768203735
keywords[6].display_name	Operator (biology)
keywords[7].id	https://openalex.org/keywords/linear-differential-equation
keywords[7].score	0.47095733880996704
keywords[7].display_name	Linear differential equation
keywords[8].id	https://openalex.org/keywords/differential
keywords[8].score	0.46367785334587097
keywords[8].display_name	Differential (mechanical device)
keywords[9].id	https://openalex.org/keywords/type
keywords[9].score	0.4539681077003479
keywords[9].display_name	Type (biology)
keywords[10].id	https://openalex.org/keywords/differential-equation
keywords[10].score	0.4364592432975769
keywords[10].display_name	Differential equation
keywords[11].id	https://openalex.org/keywords/canonical-form
keywords[11].score	0.42875000834465027
keywords[11].display_name	Canonical form
keywords[12].id	https://openalex.org/keywords/mathematical-analysis
keywords[12].score	0.27854496240615845
keywords[12].display_name	Mathematical analysis
keywords[13].id	https://openalex.org/keywords/pure-mathematics
keywords[13].score	0.0875784158706665
keywords[13].display_name	Pure mathematics
keywords[14].id	https://openalex.org/keywords/physics
keywords[14].score	0.056616753339767456
keywords[14].display_name	Physics
language	en
locations[0].id	doi:10.3389/fams.2024.1384559
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S2597085352
locations[0].source.issn	2297-4687
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2297-4687
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	Frontiers in Applied Mathematics and Statistics
locations[0].source.host_organization	https://openalex.org/P4310320527
locations[0].source.host_organization_name	Frontiers Media
locations[0].source.host_organization_lineage	https://openalex.org/P4310320527
locations[0].source.host_organization_lineage_names	Frontiers Media
locations[0].license	cc-by
locations[0].pdf_url	https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf
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	Frontiers in Applied Mathematics and Statistics
locations[0].landing_page_url	https://doi.org/10.3389/fams.2024.1384559
locations[1].id	pmh:oai:doaj.org/article:50a46ee73ca3485885b0e73c8292e3ff
locations[1].is_oa	False
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
locations[1].pdf_url
locations[1].version	submittedVersion
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published	False
locations[1].raw_source_name	Frontiers in Applied Mathematics and Statistics, Vol 10 (2024)
locations[1].landing_page_url	https://doaj.org/article/50a46ee73ca3485885b0e73c8292e3ff
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5100653748
authorships[0].author.orcid	https://orcid.org/0009-0002-7989-0466
authorships[0].author.display_name	Ahmed M. Hassan
authorships[0].countries	EG
authorships[0].affiliations[0].institution_ids	https://openalex.org/I207547235
authorships[0].affiliations[0].raw_affiliation_string	Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
authorships[0].institutions[0].id	https://openalex.org/I207547235
authorships[0].institutions[0].ror	https://ror.org/03tn5ee41
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I207547235
authorships[0].institutions[0].country_code	EG
authorships[0].institutions[0].display_name	Benha University
authorships[0].author_position	first
authorships[0].raw_author_name	Ahmed M. Hassan
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
authorships[1].author.id	https://openalex.org/A5074973583
authorships[1].author.orcid	https://orcid.org/0000-0003-3850-1022
authorships[1].author.display_name	Osama Moaaz
authorships[1].countries	EG, IT
authorships[1].affiliations[0].institution_ids	https://openalex.org/I4210155399
authorships[1].affiliations[0].raw_affiliation_string	Section of Mathematics, International Telematic University Uninettuno, Rome, Italy
authorships[1].affiliations[1].institution_ids	https://openalex.org/I159247623
authorships[1].affiliations[1].raw_affiliation_string	Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
authorships[1].institutions[0].id	https://openalex.org/I159247623
authorships[1].institutions[0].ror	https://ror.org/01k8vtd75
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I159247623
authorships[1].institutions[0].country_code	EG
authorships[1].institutions[0].display_name	Mansoura University
authorships[1].institutions[1].id	https://openalex.org/I4210155399
authorships[1].institutions[1].ror	https://ror.org/04q0nep37
authorships[1].institutions[1].type	education
authorships[1].institutions[1].lineage	https://openalex.org/I4210155399
authorships[1].institutions[1].country_code	IT
authorships[1].institutions[1].display_name	UniNettuno University
authorships[1].author_position	middle
authorships[1].raw_author_name	Osama Moaaz
authorships[1].is_corresponding	True
authorships[1].raw_affiliation_strings	Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt, Section of Mathematics, International Telematic University Uninettuno, Rome, Italy
authorships[2].author.id	https://openalex.org/A5088545047
authorships[2].author.orcid	https://orcid.org/0000-0002-1167-2430
authorships[2].author.display_name	Sameh Askar
authorships[2].countries	SA
authorships[2].affiliations[0].institution_ids	https://openalex.org/I28022161
authorships[2].affiliations[0].raw_affiliation_string	Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia
authorships[2].institutions[0].id	https://openalex.org/I28022161
authorships[2].institutions[0].ror	https://ror.org/02f81g417
authorships[2].institutions[0].type	education
authorships[2].institutions[0].lineage	https://openalex.org/I28022161
authorships[2].institutions[0].country_code	SA
authorships[2].institutions[0].display_name	King Saud University
authorships[2].author_position	middle
authorships[2].raw_author_name	Sameh S. Askar
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia
authorships[3].author.id	https://openalex.org/A5018298333
authorships[3].author.orcid	https://orcid.org/0000-0001-7103-8872
authorships[3].author.display_name	Ahmad M. Alshamrani
authorships[3].countries	SA
authorships[3].affiliations[0].institution_ids	https://openalex.org/I28022161
authorships[3].affiliations[0].raw_affiliation_string	Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia
authorships[3].institutions[0].id	https://openalex.org/I28022161
authorships[3].institutions[0].ror	https://ror.org/02f81g417
authorships[3].institutions[0].type	education
authorships[3].institutions[0].lineage	https://openalex.org/I28022161
authorships[3].institutions[0].country_code	SA
authorships[3].institutions[0].display_name	King Saud University
authorships[3].author_position	last
authorships[3].raw_author_name	Ahmad M. Alshamrani
authorships[3].is_corresponding	False
authorships[3].raw_affiliation_strings	Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia
has_content.pdf	True
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Oscillatory behavior of solutions of second-order non-linear differential equations with mixed non-linear neutral terms
has_fulltext	False
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	0.9998000264167786
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/W2048668592, https://openalex.org/W2123585262, https://openalex.org/W2093338910, https://openalex.org/W2937301577, https://openalex.org/W2062635734, https://openalex.org/W2375520694, https://openalex.org/W3176473605, https://openalex.org/W2367945514, https://openalex.org/W3119112359, https://openalex.org/W258802313
cited_by_count	0
locations_count	2
best_oa_location.id	doi:10.3389/fams.2024.1384559
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S2597085352
best_oa_location.source.issn	2297-4687
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2297-4687
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	Frontiers in Applied Mathematics and Statistics
best_oa_location.source.host_organization	https://openalex.org/P4310320527
best_oa_location.source.host_organization_name	Frontiers Media
best_oa_location.source.host_organization_lineage	https://openalex.org/P4310320527
best_oa_location.source.host_organization_lineage_names	Frontiers Media
best_oa_location.license	cc-by
best_oa_location.pdf_url	https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf
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	Frontiers in Applied Mathematics and Statistics
best_oa_location.landing_page_url	https://doi.org/10.3389/fams.2024.1384559
primary_location.id	doi:10.3389/fams.2024.1384559
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S2597085352
primary_location.source.issn	2297-4687
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2297-4687
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	Frontiers in Applied Mathematics and Statistics
primary_location.source.host_organization	https://openalex.org/P4310320527
primary_location.source.host_organization_name	Frontiers Media
primary_location.source.host_organization_lineage	https://openalex.org/P4310320527
primary_location.source.host_organization_lineage_names	Frontiers Media
primary_location.license	cc-by
primary_location.pdf_url	https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1384559/pdf
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	Frontiers in Applied Mathematics and Statistics
primary_location.landing_page_url	https://doi.org/10.3389/fams.2024.1384559
publication_date	2024-07-16
publication_year	2024
referenced_works	https://openalex.org/W163144314, https://openalex.org/W2029651239, https://openalex.org/W1968736196, https://openalex.org/W2004693192, https://openalex.org/W4280636746, https://openalex.org/W4398237552, https://openalex.org/W3182490320, https://openalex.org/W3034372617, https://openalex.org/W6604433705, https://openalex.org/W2948129171, https://openalex.org/W4389887934, https://openalex.org/W2188765805, https://openalex.org/W6766993195, https://openalex.org/W3012487426, https://openalex.org/W3037268225, https://openalex.org/W2295437805, https://openalex.org/W3141785521, https://openalex.org/W2004604977, https://openalex.org/W2006505167, https://openalex.org/W2751107753, https://openalex.org/W2351992725, https://openalex.org/W2051475153, https://openalex.org/W644543390, https://openalex.org/W2968552280, https://openalex.org/W4248179338, https://openalex.org/W607066590
referenced_works_count	26
abstract_inverted_index.by	9
abstract_inverted_index.in	24, 61
abstract_inverted_index.of	14, 27, 39, 57, 74
abstract_inverted_index.to	4, 52, 69
abstract_inverted_index.The	31
abstract_inverted_index.and	20, 45, 55
abstract_inverted_index.are	34, 67
abstract_inverted_index.the	25, 28, 37, 40, 62, 71, 75
abstract_inverted_index.This	0
abstract_inverted_index.both	18
abstract_inverted_index.case	26
abstract_inverted_index.from	36
abstract_inverted_index.lead	51
abstract_inverted_index.upon	6
abstract_inverted_index.These	49
abstract_inverted_index.delay	19
abstract_inverted_index.found	60
abstract_inverted_index.mixed	15
abstract_inverted_index.seeks	3
abstract_inverted_index.study	1
abstract_inverted_index.these	7
abstract_inverted_index.type,	16
abstract_inverted_index.expand	5
abstract_inverted_index.terms,	22
abstract_inverted_index.Riccati	43
abstract_inverted_index.derived	35
abstract_inverted_index.method,	42
abstract_inverted_index.neutral	11
abstract_inverted_index.results	33, 59
abstract_inverted_index.advanced	21
abstract_inverted_index.examples	66
abstract_inverted_index.existing	58
abstract_inverted_index.integral	46
abstract_inverted_index.provided	68
abstract_inverted_index.averaging	47
abstract_inverted_index.canonical	29
abstract_inverted_index.criteria.	77
abstract_inverted_index.developed	76
abstract_inverted_index.equations	13
abstract_inverted_index.operator.	30
abstract_inverted_index.practical	72
abstract_inverted_index.presented	32
abstract_inverted_index.primarily	2
abstract_inverted_index.comparison	41
abstract_inverted_index.extensions	56
abstract_inverted_index.technique.	48
abstract_inverted_index.application	38
abstract_inverted_index.demonstrate	70
abstract_inverted_index.literature.	63
abstract_inverted_index.substantial	53
abstract_inverted_index.developments	8
abstract_inverted_index.differential	12
abstract_inverted_index.encompassing	10
abstract_inverted_index.illustrative	65
abstract_inverted_index.implications	73
abstract_inverted_index.improvements	54
abstract_inverted_index.particularly	23
abstract_inverted_index.Additionally,	64
abstract_inverted_index.incorporating	17
abstract_inverted_index.methodologies	50
abstract_inverted_index.transformation,	44
cited_by_percentile_year
corresponding_author_ids	https://openalex.org/A5074973583
countries_distinct_count	3
institutions_distinct_count	4
corresponding_institution_ids	https://openalex.org/I159247623, https://openalex.org/I4210155399
sustainable_development_goals[0].id	https://metadata.un.org/sdg/17
sustainable_development_goals[0].score	0.41999998688697815
sustainable_development_goals[0].display_name	Partnerships for the goals
citation_normalized_percentile.value	0.15052773
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False