{"id":"https://openalex.org/W3010887263","doi":"https://doi.org/10.3390/math8030422","title":"Global Mittag\u2013Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks","display_name":"Global Mittag\u2013Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks","publication_year":2020,"publication_date":"2020-03-14","ids":{"openalex":"https://openalex.org/W3010887263","doi":"https://doi.org/10.3390/math8030422","mag":"3010887263"},"language":"en","primary_location":{"id":"doi:10.3390/math8030422","doi":"https://doi.org/10.3390/math8030422","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8030422","pdf_url":"https://www.mdpi.com/2227-7390/8/3/422/pdf?version=1585284613","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/8/3/422/pdf?version=1585284613","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035006871","display_name":"Grienggrai Rajchakit","orcid":"https://orcid.org/0000-0001-6053-6219","observed_orcids":["https://orcid.org/0000-0001-6053-6219"]},"institutions":[{"id":"https://openalex.org/I190734841","display_name":"Maejo University","ror":"https://ror.org/03c7s1f64","country_code":"TH","type":"education","lineage":["https://openalex.org/I190734841"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Grienggrai Rajchakit","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand"],"raw_orcid":"https://orcid.org/0000-0001-6053-6219","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand","institution_ids":["https://openalex.org/I190734841"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077341019","display_name":"Pharunyou Chanthorn","orcid":"https://orcid.org/0000-0002-0130-9304","observed_orcids":["https://orcid.org/0000-0002-0130-9304"]},"institutions":[{"id":"https://openalex.org/I48076826","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25","country_code":"TH","type":"education","lineage":["https://openalex.org/I48076826"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Pharunyou Chanthorn","raw_affiliation_strings":["Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand","institution_ids":["https://openalex.org/I48076826"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061562396","display_name":"Pramet Kaewmesri","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60837268","display_name":"King Mongkut's University of Technology Thonburi","ror":"https://ror.org/0057ax056","country_code":"TH","type":"education","lineage":["https://openalex.org/I60837268"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Pramet Kaewmesri","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand","institution_ids":["https://openalex.org/I60837268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086901177","display_name":"Ramalingam Sriraman","orcid":"https://orcid.org/0000-0002-6301-654X","observed_orcids":["https://orcid.org/0000-0002-6301-654X"]},"institutions":[{"id":"https://openalex.org/I1330855593","display_name":"Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology","ror":"https://ror.org/05bc5bx80","country_code":"IN","type":"education","lineage":["https://openalex.org/I1330855593"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramalingam Sriraman","raw_affiliation_strings":["Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India","institution_ids":["https://openalex.org/I1330855593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072923302","display_name":"Chee Peng Lim","orcid":"https://orcid.org/0000-0003-4191-9083","observed_orcids":["https://orcid.org/0000-0003-4191-9083"]},"institutions":[{"id":"https://openalex.org/I149704539","display_name":"Deakin University","ror":"https://ror.org/02czsnj07","country_code":"AU","type":"education","lineage":["https://openalex.org/I149704539"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Chee Peng Lim","raw_affiliation_strings":["Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia","institution_ids":["https://openalex.org/I149704539"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5035006871"],"corresponding_institution_ids":["https://openalex.org/I190734841"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1267},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1267},"fwci":6.7059,"has_fulltext":true,"cited_by_count":118,"citation_normalized_percentile":{"value":0.97766992,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"8","issue":"3","first_page":"422","last_page":"422"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-order-neural-networks","display_name":"fractional-order neural networks","score":0.7229999899864197},{"id":"https://openalex.org/keywords/quaternion-valued-neural-networks","display_name":"quaternion-valued neural networks","score":0.972000002861023},{"id":"https://openalex.org/keywords/memristive-neural-networks","display_name":"memristive neural networks","score":0.9929999709129333},{"id":"https://openalex.org/keywords/state-feedback-stabilization","display_name":"state feedback stabilization","score":0.7960000038146973},{"id":"https://openalex.org/keywords/set-valued-mappings","display_name":"set-valued mappings","score":0.968999981880188}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.884901762008667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6650883555412292},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6574913859367371},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6066989302635193},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5083634257316589},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4861871600151062},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4613744020462036},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4427958130836487},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43049055337905884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4079931676387787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28433144092559814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21196812391281128},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15511620044708252},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11348658800125122},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07723724842071533},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/math8030422","doi":"https://doi.org/10.3390/math8030422","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8030422","pdf_url":"https://www.mdpi.com/2227-7390/8/3/422/pdf?version=1585284613","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:8:y:2020:i:3:p:422-:d:332701","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/8/3/422/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:0d2cc7a76209463ca9fc22a72529aaa2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/0d2cc7a76209463ca9fc22a72529aaa2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 8, Iss 3, p 422 (2020)","raw_type":"article"},{"id":"pmh:oai:dro.deakin.edu.au:DU:30136153","doi":null,"is_oa":false,"landing_page_url":"http://doi.org/10.3390/math8030422","pdf_url":null,"source":{"id":"https://openalex.org/S4306401102","display_name":"Own your potential (DEAKIN)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149704539","host_organization_name":"Deakin University","host_organization_lineage":["https://openalex.org/I149704539"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:figshare.com:article/20709286","doi":null,"is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Global_mittag-leffler_stability_and_stabilization_analysis_of_fractional-order_quaternion-valued_memristive_neural_networks/20709286","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/math8030422","doi":"https://doi.org/10.3390/math8030422","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8030422","pdf_url":"https://www.mdpi.com/2227-7390/8/3/422/pdf?version=1585284613","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321529","display_name":"Chiang Mai University","ror":"https://ror.org/05m2fqn25"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010887263.pdf","grobid_xml":"https://content.openalex.org/works/W3010887263.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1514218977","https://openalex.org/W1522745717","https://openalex.org/W1592648094","https://openalex.org/W1975003303","https://openalex.org/W1990375062","https://openalex.org/W1995314879","https://openalex.org/W2016812413","https://openalex.org/W2016922062","https://openalex.org/W2030147677","https://openalex.org/W2030834420","https://openalex.org/W2033772417","https://openalex.org/W2042330780","https://openalex.org/W2047063224","https://openalex.org/W2063133641","https://openalex.org/W2080625874","https://openalex.org/W2112181056","https://openalex.org/W2162651880","https://openalex.org/W2170810674","https://openalex.org/W2210337553","https://openalex.org/W2301703807","https://openalex.org/W2344164154","https://openalex.org/W2515469213","https://openalex.org/W2516728239","https://openalex.org/W2606767684","https://openalex.org/W2614570124","https://openalex.org/W2742855059","https://openalex.org/W2743408846","https://openalex.org/W2754630447","https://openalex.org/W2793034572","https://openalex.org/W2800372837","https://openalex.org/W2840983261","https://openalex.org/W2885819890","https://openalex.org/W2892356487","https://openalex.org/W2895789449","https://openalex.org/W2909399868","https://openalex.org/W2944535583","https://openalex.org/W2963690555","https://openalex.org/W2967802572","https://openalex.org/W2987253914","https://openalex.org/W2990566453","https://openalex.org/W2990694306","https://openalex.org/W2996019815","https://openalex.org/W4210718478","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W4322766131","https://openalex.org/W2990694306","https://openalex.org/W3178648323","https://openalex.org/W4286697024","https://openalex.org/W4207042048","https://openalex.org/W4367043464","https://openalex.org/W3008368578","https://openalex.org/W2800372837","https://openalex.org/W2840983261","https://openalex.org/W2953563516"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,29,34,39,53,83],"global":[4,65],"Mittag\u2013Leffler":[5,66],"stability":[6,67],"and":[7,68],"stabilization":[8,69],"analysis":[9],"of":[10,36,55,71,85],"fractional-order":[11,41,48,57,59],"quaternion-valued":[12,42],"memristive":[13],"neural":[14],"networks":[15],"(FOQVMNNs).":[16],"The":[17],"state":[18],"feedback":[19],"stabilizing":[20],"control":[21],"law":[22],"is":[23,44],"designed":[24],"in":[25],"order":[26],"to":[27,81],"stabilize":[28],"considered":[30,72],"problem.":[31],"Based":[32],"on":[33],"non-commutativity":[35],"quaternion":[37],"multiplication,":[38],"original":[40],"systems":[43],"divided":[45],"into":[46],"four":[47],"real-valued":[49],"systems.":[50],"By":[51],"using":[52],"method":[54],"Lyapunov":[56],"derivative,":[58],"differential":[60],"inclusions,":[61],"set-valued":[62],"maps,":[63],"several":[64],"conditions":[70],"FOQVMNNs":[73],"are":[74,79],"established.":[75],"Two":[76],"numerical":[77],"examples":[78],"provided":[80],"illustrate":[82],"usefulness":[84],"our":[86],"analytical":[87],"results.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":29},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":10}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-03-23T00:00:00"}