New Approach to Quasi-Synchronization of Fractional-Order Delayed Neural Networks Article Swipe

PDF

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.3390/fractalfract7110825

This article investigates quasi-synchronization for a class of fractional-order delayed neural networks. By utilizing the properties of the Laplace transform, the Caputo derivative, and the Mittag–Leffler function, a new fractional-order differential inequality is introduced. Furthermore, an adaptive controller is designed, resulting in the derivation of an effective criterion to ensure the aforementioned synchronization. Finally, a numerical illustration is provided to demonstrate the validity of the presented theoretical findings.

Related Topics

Computer Science

Mathematics

Mathematical Analysis

Artificial Intelligence

Concepts

Laplace transform Synchronization (alternating current) Fractional calculus Artificial neural network Control theory (sociology) Controller (irrigation) Order (exchange) Computer science Class (philosophy) Function (biology) Mathematics Applied mathematics Topology (electrical circuits) Mathematical analysis Control (management) Artificial intelligence Combinatorics Economics Evolutionary biology Finance Biology Agronomy

Metadata

Type: article
Language: en
Landing Page: https://doi.org/10.3390/fractalfract7110825
PDF: https://www.mdpi.com/2504-3110/7/11/825/pdf?version=1700108940
OA Status: gold
Cited By: 1
References: 51
Related Works: 10
OpenAlex ID: https://openalex.org/W4388734537

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4388734537

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.3390/fractalfract7110825

Digital Object Identifier
Title: New Approach to Quasi-Synchronization of Fractional-Order Delayed Neural Networks

Work title
Type: article

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-11-16

Full publication date if available
Authors: Shilong Zhang, Feifei Du, Diyi Chen

List of authors in order
Landing page: https://doi.org/10.3390/fractalfract7110825

Publisher landing page
PDF URL: https://www.mdpi.com/2504-3110/7/11/825/pdf?version=1700108940

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/2504-3110/7/11/825/pdf?version=1700108940

Direct OA link when available
Concepts: Laplace transform, Synchronization (alternating current), Fractional calculus, Artificial neural network, Control theory (sociology), Controller (irrigation), Order (exchange), Computer science, Class (philosophy), Function (biology), Mathematics, Applied mathematics, Topology (electrical circuits), Mathematical analysis, Control (management), Artificial intelligence, Combinatorics, Economics, Evolutionary biology, Finance, Biology, Agronomy

Top concepts (fields/topics) attached by OpenAlex
Cited by: 1

Total citation count in OpenAlex
Citations by year (recent): 2024: 1

Per-year citation counts (last 5 years)
References (count): 51

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

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4388734537
doi	https://doi.org/10.3390/fractalfract7110825
ids.doi	https://doi.org/10.3390/fractalfract7110825
ids.openalex	https://openalex.org/W4388734537
fwci	0.43955229
type	article
title	New Approach to Quasi-Synchronization of Fractional-Order Delayed Neural Networks
awards[0].id	https://openalex.org/G3062946738
awards[0].funder_id	https://openalex.org/F4320334997
awards[0].display_name
awards[0].funder_award_id	2452022176
awards[0].funder_display_name	Chinese Universities Scientific Fund
biblio.issue	11
biblio.volume	7
biblio.last_page	825
biblio.first_page	825
topics[0].id	https://openalex.org/T11347
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	1.0
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1705
topics[0].subfield.display_name	Computer Networks and Communications
topics[0].display_name	Neural Networks Stability and Synchronization
topics[1].id	https://openalex.org/T11513
topics[1].field.id	https://openalex.org/fields/31
topics[1].field.display_name	Physics and Astronomy
topics[1].score	0.9995999932289124
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/3109
topics[1].subfield.display_name	Statistical and Nonlinear Physics
topics[1].display_name	stochastic dynamics and bifurcation
topics[2].id	https://openalex.org/T11187
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.998199999332428
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1705
topics[2].subfield.display_name	Computer Networks and Communications
topics[2].display_name	Nonlinear Dynamics and Pattern Formation
funders[0].id	https://openalex.org/F4320334997
funders[0].ror
funders[0].display_name	Chinese Universities Scientific Fund
is_xpac	False
apc_list.value	1600
apc_list.currency	CHF
apc_list.value_usd	1732
apc_paid.value	1600
apc_paid.currency	CHF
apc_paid.value_usd	1732
concepts[0].id	https://openalex.org/C97937538
concepts[0].level	2
concepts[0].score	0.7640025615692139
concepts[0].wikidata	https://www.wikidata.org/wiki/Q199691
concepts[0].display_name	Laplace transform
concepts[1].id	https://openalex.org/C2778562939
concepts[1].level	3
concepts[1].score	0.7481307983398438
concepts[1].wikidata	https://www.wikidata.org/wiki/Q1298791
concepts[1].display_name	Synchronization (alternating current)
concepts[2].id	https://openalex.org/C154249771
concepts[2].level	2
concepts[2].score	0.6525158286094666
concepts[2].wikidata	https://www.wikidata.org/wiki/Q1339058
concepts[2].display_name	Fractional calculus
concepts[3].id	https://openalex.org/C50644808
concepts[3].level	2
concepts[3].score	0.5645737648010254
concepts[3].wikidata	https://www.wikidata.org/wiki/Q192776
concepts[3].display_name	Artificial neural network
concepts[4].id	https://openalex.org/C47446073
concepts[4].level	3
concepts[4].score	0.5607993006706238
concepts[4].wikidata	https://www.wikidata.org/wiki/Q5165890
concepts[4].display_name	Control theory (sociology)
concepts[5].id	https://openalex.org/C203479927
concepts[5].level	2
concepts[5].score	0.5482202768325806
concepts[5].wikidata	https://www.wikidata.org/wiki/Q5165939
concepts[5].display_name	Controller (irrigation)
concepts[6].id	https://openalex.org/C182306322
concepts[6].level	2
concepts[6].score	0.5024263858795166
concepts[6].wikidata	https://www.wikidata.org/wiki/Q1779371
concepts[6].display_name	Order (exchange)
concepts[7].id	https://openalex.org/C41008148
concepts[7].level	0
concepts[7].score	0.4774808883666992
concepts[7].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[7].display_name	Computer science
concepts[8].id	https://openalex.org/C2777212361
concepts[8].level	2
concepts[8].score	0.4762932360172272
concepts[8].wikidata	https://www.wikidata.org/wiki/Q5127848
concepts[8].display_name	Class (philosophy)
concepts[9].id	https://openalex.org/C14036430
concepts[9].level	2
concepts[9].score	0.4469022750854492
concepts[9].wikidata	https://www.wikidata.org/wiki/Q3736076
concepts[9].display_name	Function (biology)
concepts[10].id	https://openalex.org/C33923547
concepts[10].level	0
concepts[10].score	0.40874525904655457
concepts[10].wikidata	https://www.wikidata.org/wiki/Q395
concepts[10].display_name	Mathematics
concepts[11].id	https://openalex.org/C28826006
concepts[11].level	1
concepts[11].score	0.36677002906799316
concepts[11].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[11].display_name	Applied mathematics
concepts[12].id	https://openalex.org/C184720557
concepts[12].level	2
concepts[12].score	0.23657923936843872
concepts[12].wikidata	https://www.wikidata.org/wiki/Q7825049
concepts[12].display_name	Topology (electrical circuits)
concepts[13].id	https://openalex.org/C134306372
concepts[13].level	1
concepts[13].score	0.11377963423728943
concepts[13].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[13].display_name	Mathematical analysis
concepts[14].id	https://openalex.org/C2775924081
concepts[14].level	2
concepts[14].score	0.10464653372764587
concepts[14].wikidata	https://www.wikidata.org/wiki/Q55608371
concepts[14].display_name	Control (management)
concepts[15].id	https://openalex.org/C154945302
concepts[15].level	1
concepts[15].score	0.09951654076576233
concepts[15].wikidata	https://www.wikidata.org/wiki/Q11660
concepts[15].display_name	Artificial intelligence
concepts[16].id	https://openalex.org/C114614502
concepts[16].level	1
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[16].display_name	Combinatorics
concepts[17].id	https://openalex.org/C162324750
concepts[17].level	0
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q8134
concepts[17].display_name	Economics
concepts[18].id	https://openalex.org/C78458016
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q840400
concepts[18].display_name	Evolutionary biology
concepts[19].id	https://openalex.org/C10138342
concepts[19].level	1
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q43015
concepts[19].display_name	Finance
concepts[20].id	https://openalex.org/C86803240
concepts[20].level	0
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q420
concepts[20].display_name	Biology
concepts[21].id	https://openalex.org/C6557445
concepts[21].level	1
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q173113
concepts[21].display_name	Agronomy
keywords[0].id	https://openalex.org/keywords/laplace-transform
keywords[0].score	0.7640025615692139
keywords[0].display_name	Laplace transform
keywords[1].id	https://openalex.org/keywords/synchronization
keywords[1].score	0.7481307983398438
keywords[1].display_name	Synchronization (alternating current)
keywords[2].id	https://openalex.org/keywords/fractional-calculus
keywords[2].score	0.6525158286094666
keywords[2].display_name	Fractional calculus
keywords[3].id	https://openalex.org/keywords/artificial-neural-network
keywords[3].score	0.5645737648010254
keywords[3].display_name	Artificial neural network
keywords[4].id	https://openalex.org/keywords/control-theory
keywords[4].score	0.5607993006706238
keywords[4].display_name	Control theory (sociology)
keywords[5].id	https://openalex.org/keywords/controller
keywords[5].score	0.5482202768325806
keywords[5].display_name	Controller (irrigation)
keywords[6].id	https://openalex.org/keywords/order
keywords[6].score	0.5024263858795166
keywords[6].display_name	Order (exchange)
keywords[7].id	https://openalex.org/keywords/computer-science
keywords[7].score	0.4774808883666992
keywords[7].display_name	Computer science
keywords[8].id	https://openalex.org/keywords/class
keywords[8].score	0.4762932360172272
keywords[8].display_name	Class (philosophy)
keywords[9].id	https://openalex.org/keywords/function
keywords[9].score	0.4469022750854492
keywords[9].display_name	Function (biology)
keywords[10].id	https://openalex.org/keywords/mathematics
keywords[10].score	0.40874525904655457
keywords[10].display_name	Mathematics
keywords[11].id	https://openalex.org/keywords/applied-mathematics
keywords[11].score	0.36677002906799316
keywords[11].display_name	Applied mathematics
keywords[12].id	https://openalex.org/keywords/topology
keywords[12].score	0.23657923936843872
keywords[12].display_name	Topology (electrical circuits)
keywords[13].id	https://openalex.org/keywords/mathematical-analysis
keywords[13].score	0.11377963423728943
keywords[13].display_name	Mathematical analysis
keywords[14].id	https://openalex.org/keywords/control
keywords[14].score	0.10464653372764587
keywords[14].display_name	Control (management)
keywords[15].id	https://openalex.org/keywords/artificial-intelligence
keywords[15].score	0.09951654076576233
keywords[15].display_name	Artificial intelligence
language	en
locations[0].id	doi:10.3390/fractalfract7110825
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4210227020
locations[0].source.issn	2504-3110
locations[0].source.type	journal
locations[0].source.is_oa	True
locations[0].source.issn_l	2504-3110
locations[0].source.is_core	True
locations[0].source.is_in_doaj	True
locations[0].source.display_name	Fractal and Fractional
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/2504-3110/7/11/825/pdf?version=1700108940
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	Fractal and Fractional
locations[0].landing_page_url	https://doi.org/10.3390/fractalfract7110825
locations[1].id	pmh:oai:doaj.org/article:181fa9440a9443fc8cabf1b96f4e9ef1
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	Fractal and Fractional, Vol 7, Iss 11, p 825 (2023)
locations[1].landing_page_url	https://doaj.org/article/181fa9440a9443fc8cabf1b96f4e9ef1
locations[2].id	pmh:oai:mdpi.com:/2504-3110/7/11/825/
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	Fractal and Fractional
locations[2].landing_page_url	https://dx.doi.org/10.3390/fractalfract7110825
indexed_in	crossref, doaj
authorships[0].author.id	https://openalex.org/A5100643295
authorships[0].author.orcid	https://orcid.org/0000-0003-3218-0491
authorships[0].author.display_name	Shilong Zhang
authorships[0].countries	CN
authorships[0].affiliations[0].institution_ids	https://openalex.org/I89652312
authorships[0].affiliations[0].raw_affiliation_string	College of Science, Northwest A&F University, Yangling 712100, China
authorships[0].institutions[0].id	https://openalex.org/I89652312
authorships[0].institutions[0].ror	https://ror.org/0051rme32
authorships[0].institutions[0].type	education
authorships[0].institutions[0].lineage	https://openalex.org/I89652312
authorships[0].institutions[0].country_code	CN
authorships[0].institutions[0].display_name	Northwest A&F University
authorships[0].author_position	first
authorships[0].raw_author_name	Shilong Zhang
authorships[0].is_corresponding	False
authorships[0].raw_affiliation_strings	College of Science, Northwest A&F University, Yangling 712100, China
authorships[1].author.id	https://openalex.org/A5040215010
authorships[1].author.orcid	https://orcid.org/0000-0003-4725-377X
authorships[1].author.display_name	Feifei Du
authorships[1].countries	CN
authorships[1].affiliations[0].institution_ids	https://openalex.org/I89652312
authorships[1].affiliations[0].raw_affiliation_string	College of Science, Northwest A&F University, Yangling 712100, China
authorships[1].institutions[0].id	https://openalex.org/I89652312
authorships[1].institutions[0].ror	https://ror.org/0051rme32
authorships[1].institutions[0].type	education
authorships[1].institutions[0].lineage	https://openalex.org/I89652312
authorships[1].institutions[0].country_code	CN
authorships[1].institutions[0].display_name	Northwest A&F University
authorships[1].author_position	middle
authorships[1].raw_author_name	Feifei Du
authorships[1].is_corresponding	True
authorships[1].raw_affiliation_strings	College of Science, Northwest A&F University, Yangling 712100, China
authorships[2].author.id	https://openalex.org/A5057822035
authorships[2].author.orcid	https://orcid.org/0000-0002-0609-0129
authorships[2].author.display_name	Diyi Chen
authorships[2].countries	CN
authorships[2].affiliations[0].institution_ids	https://openalex.org/I4210092032, https://openalex.org/I89652312
authorships[2].affiliations[0].raw_affiliation_string	Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling 712100, China
authorships[2].institutions[0].id	https://openalex.org/I4210092032
authorships[2].institutions[0].ror	https://ror.org/00m4czf33
authorships[2].institutions[0].type	facility
authorships[2].institutions[0].lineage	https://openalex.org/I4210092032
authorships[2].institutions[0].country_code	CN
authorships[2].institutions[0].display_name	China Institute of Water Resources and Hydropower Research
authorships[2].institutions[1].id	https://openalex.org/I89652312
authorships[2].institutions[1].ror	https://ror.org/0051rme32
authorships[2].institutions[1].type	education
authorships[2].institutions[1].lineage	https://openalex.org/I89652312
authorships[2].institutions[1].country_code	CN
authorships[2].institutions[1].display_name	Northwest A&F University
authorships[2].author_position	last
authorships[2].raw_author_name	Diyi Chen
authorships[2].is_corresponding	False
authorships[2].raw_affiliation_strings	Institute of Water Resources and Hydropower Research, Northwest A&F University, Yangling 712100, China
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/2504-3110/7/11/825/pdf?version=1700108940
open_access.oa_status	gold
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	New Approach to Quasi-Synchronization of Fractional-Order Delayed Neural Networks
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T03:46:38.306776
primary_topic.id	https://openalex.org/T11347
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	1.0
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1705
primary_topic.subfield.display_name	Computer Networks and Communications
primary_topic.display_name	Neural Networks Stability and Synchronization
related_works	https://openalex.org/W2082446734, https://openalex.org/W3148881609, https://openalex.org/W4313560640, https://openalex.org/W4235050982, https://openalex.org/W4246784705, https://openalex.org/W2350962908, https://openalex.org/W2253351617, https://openalex.org/W3024206168, https://openalex.org/W4317627639, https://openalex.org/W3005643231
cited_by_count	1
counts_by_year[0].year	2024
counts_by_year[0].cited_by_count	1
locations_count	3
best_oa_location.id	doi:10.3390/fractalfract7110825
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4210227020
best_oa_location.source.issn	2504-3110
best_oa_location.source.type	journal
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l	2504-3110
best_oa_location.source.is_core	True
best_oa_location.source.is_in_doaj	True
best_oa_location.source.display_name	Fractal and Fractional
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/2504-3110/7/11/825/pdf?version=1700108940
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	Fractal and Fractional
best_oa_location.landing_page_url	https://doi.org/10.3390/fractalfract7110825
primary_location.id	doi:10.3390/fractalfract7110825
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4210227020
primary_location.source.issn	2504-3110
primary_location.source.type	journal
primary_location.source.is_oa	True
primary_location.source.issn_l	2504-3110
primary_location.source.is_core	True
primary_location.source.is_in_doaj	True
primary_location.source.display_name	Fractal and Fractional
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/2504-3110/7/11/825/pdf?version=1700108940
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	Fractal and Fractional
primary_location.landing_page_url	https://doi.org/10.3390/fractalfract7110825
publication_date	2023-11-16
publication_year	2023
referenced_works	https://openalex.org/W2025068047, https://openalex.org/W2294239831, https://openalex.org/W2414109456, https://openalex.org/W2111271983, https://openalex.org/W2101404214, https://openalex.org/W2016570436, https://openalex.org/W1983854366, https://openalex.org/W2072789018, https://openalex.org/W6677225333, https://openalex.org/W1991965806, https://openalex.org/W2139363317, https://openalex.org/W2015735099, https://openalex.org/W2952845113, https://openalex.org/W2996019815, https://openalex.org/W2104454795, https://openalex.org/W1970680382, https://openalex.org/W2060927950, https://openalex.org/W2070504163, https://openalex.org/W2584576269, https://openalex.org/W2112246162, https://openalex.org/W1968134101, https://openalex.org/W2204225973, https://openalex.org/W2008244590, https://openalex.org/W3035617291, https://openalex.org/W1975003303, https://openalex.org/W2086087072, https://openalex.org/W1992749072, https://openalex.org/W4252416079, https://openalex.org/W1974582083, https://openalex.org/W2901304015, https://openalex.org/W3080490719, https://openalex.org/W3157741549, https://openalex.org/W2979534084, https://openalex.org/W2043345530, https://openalex.org/W2883863415, https://openalex.org/W2214962116, https://openalex.org/W2580848314, https://openalex.org/W2806387984, https://openalex.org/W2765475579, https://openalex.org/W2775822061, https://openalex.org/W4319301773, https://openalex.org/W2945854435, https://openalex.org/W2037826562, https://openalex.org/W3203583012, https://openalex.org/W4247953052, https://openalex.org/W342691465, https://openalex.org/W3093926078, https://openalex.org/W3000980125, https://openalex.org/W2085136674, https://openalex.org/W2116973981, https://openalex.org/W3099308307
referenced_works_count	51
abstract_inverted_index.a	5, 27, 54
abstract_inverted_index.By	12
abstract_inverted_index.an	35, 45
abstract_inverted_index.in	41
abstract_inverted_index.is	32, 38, 57
abstract_inverted_index.of	7, 16, 44, 63
abstract_inverted_index.to	48, 59
abstract_inverted_index.and	23
abstract_inverted_index.for	4
abstract_inverted_index.new	28
abstract_inverted_index.the	14, 17, 20, 24, 42, 50, 61, 64
abstract_inverted_index.This	0
abstract_inverted_index.class	6
abstract_inverted_index.Caputo	21
abstract_inverted_index.ensure	49
abstract_inverted_index.neural	10
abstract_inverted_index.Laplace	18
abstract_inverted_index.article	1
abstract_inverted_index.delayed	9
abstract_inverted_index.Finally,	53
abstract_inverted_index.adaptive	36
abstract_inverted_index.provided	58
abstract_inverted_index.validity	62
abstract_inverted_index.criterion	47
abstract_inverted_index.designed,	39
abstract_inverted_index.effective	46
abstract_inverted_index.findings.	67
abstract_inverted_index.function,	26
abstract_inverted_index.networks.	11
abstract_inverted_index.numerical	55
abstract_inverted_index.presented	65
abstract_inverted_index.resulting	40
abstract_inverted_index.utilizing	13
abstract_inverted_index.controller	37
abstract_inverted_index.derivation	43
abstract_inverted_index.inequality	31
abstract_inverted_index.properties	15
abstract_inverted_index.transform,	19
abstract_inverted_index.demonstrate	60
abstract_inverted_index.derivative,	22
abstract_inverted_index.introduced.	33
abstract_inverted_index.theoretical	66
abstract_inverted_index.Furthermore,	34
abstract_inverted_index.differential	30
abstract_inverted_index.illustration	56
abstract_inverted_index.investigates	2
abstract_inverted_index.aforementioned	51
abstract_inverted_index.Mittag–Leffler	25
abstract_inverted_index.fractional-order	8, 29
abstract_inverted_index.synchronization.	52
abstract_inverted_index.quasi-synchronization	3
cited_by_percentile_year.max	94
cited_by_percentile_year.min	90
corresponding_author_ids	https://openalex.org/A5040215010
countries_distinct_count	1
institutions_distinct_count	3
corresponding_institution_ids	https://openalex.org/I89652312
sustainable_development_goals[0].id	https://metadata.un.org/sdg/10
sustainable_development_goals[0].score	0.5
sustainable_development_goals[0].display_name	Reduced inequalities
citation_normalized_percentile.value	0.55319814
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False