{"id":"https://openalex.org/W2726425083","doi":"https://doi.org/10.3846/13926292.2017.1329755","title":"Correction: FRACTIONAL ORDER BARBALAT\u2019S LEMMA AND ITS APPLICATIONS IN THE STABILITY OF FRACTIONAL ORDER NONLINEAR SYSTEMS","display_name":"Correction: FRACTIONAL ORDER BARBALAT\u2019S LEMMA AND ITS APPLICATIONS IN THE STABILITY OF FRACTIONAL ORDER NONLINEAR SYSTEMS","publication_year":2017,"publication_date":"2017-07-03","ids":{"openalex":"https://openalex.org/W2726425083","doi":"https://doi.org/10.3846/13926292.2017.1329755","mag":"2726425083"},"language":"en","primary_location":{"id":"doi:10.3846/13926292.2017.1329755","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1329755","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/909/690","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"type":"erratum","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.vgtu.lt/index.php/MMA/article/download/909/690","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029200638","display_name":"Fei Wang","orcid":"https://orcid.org/0000-0002-2952-4911"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Wang","raw_affiliation_strings":["Jiangnan University","School of Internet of Things, Jiangnan University, 214122 Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangnan University","institution_ids":["https://openalex.org/I111599522"]},{"raw_affiliation_string":"School of Internet of Things, Jiangnan University, 214122 Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077060852","display_name":"Yongqing Yang","orcid":"https://orcid.org/0000-0002-8172-6473"},"institutions":[{"id":"https://openalex.org/I111599522","display_name":"Jiangnan University","ror":"https://ror.org/04mkzax54","country_code":"CN","type":"education","lineage":["https://openalex.org/I111599522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongqing Yang","raw_affiliation_strings":["Jiangnan University","School of Science, Jiangnan University, 214122 Wuxi, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangnan University","institution_ids":["https://openalex.org/I111599522"]},{"raw_affiliation_string":"School of Science, Jiangnan University, 214122 Wuxi, China","institution_ids":["https://openalex.org/I111599522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111599522"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"4","first_page":"503","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9987000226974487,"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/T10244","display_name":"Chaos control and synchronization","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.892180323600769},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.8191372752189636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7175750136375427},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6621138453483582},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6436307430267334},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5184361934661865},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5132575035095215},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43004053831100464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3688298463821411},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11710608005523682},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06840330362319946}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.892180323600769},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8191372752189636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7175750136375427},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6621138453483582},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6436307430267334},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5184361934661865},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5132575035095215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43004053831100464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3688298463821411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11710608005523682},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06840330362319946},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3846/13926292.2017.1329755","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1329755","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/909/690","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:57f47a8450884079b9dbc8fab58b55ad","is_oa":false,"landing_page_url":"https://doaj.org/article/57f47a8450884079b9dbc8fab58b55ad","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Modelling and Analysis, Vol 22, Iss 4 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3846/13926292.2017.1329755","is_oa":true,"landing_page_url":"https://doi.org/10.3846/13926292.2017.1329755","pdf_url":"https://journals.vgtu.lt/index.php/MMA/article/download/909/690","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G405860530","display_name":null,"funder_award_id":"BK20161126","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2726425083.pdf","grobid_xml":"https://content.openalex.org/works/W2726425083.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W75559788","https://openalex.org/W1204148594","https://openalex.org/W1427293421","https://openalex.org/W1487127700","https://openalex.org/W1850511188","https://openalex.org/W1919710797","https://openalex.org/W1967779288","https://openalex.org/W1974820046","https://openalex.org/W1990971268","https://openalex.org/W1998561306","https://openalex.org/W2004202105","https://openalex.org/W2030959812","https://openalex.org/W2034405183","https://openalex.org/W2040966841","https://openalex.org/W2043345530","https://openalex.org/W2044167238","https://openalex.org/W2047073226","https://openalex.org/W2058095175","https://openalex.org/W2063133641","https://openalex.org/W2075069296","https://openalex.org/W2077288479","https://openalex.org/W2082446734","https://openalex.org/W2111271983","https://openalex.org/W2120827882","https://openalex.org/W2123203149","https://openalex.org/W2161456164","https://openalex.org/W2396393137"],"related_works":["https://openalex.org/W1593514994","https://openalex.org/W3203755454","https://openalex.org/W3121977679","https://openalex.org/W1494666726","https://openalex.org/W4298060673","https://openalex.org/W4312722051","https://openalex.org/W2806941034","https://openalex.org/W3096893535","https://openalex.org/W3024933985","https://openalex.org/W3158845773"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"fractional":[3,14,20,31,35,37,60],"order":[4,15,38,61],"Barbalat\u2019s":[5,39],"lemma":[6,40],"and":[7,33],"its":[8],"applications":[9],"for":[10,59],"the":[11,27,73],"stability":[12],"of":[13,53,56],"nonlinear":[16,62],"systems":[17,63],"with":[18,41],"Caputo":[19,30],"derivative":[21,32,43],"at":[22],"first.":[23],"Then,":[24],"based":[25],"on":[26],"relationship":[28],"between":[29],"Riemann-Liouville":[34,42],"derivative,":[36],"is":[44,69],"derived.":[45],"Furthermore,":[46],"according":[47],"to":[48,71],"these":[49],"results,":[50],"a":[51],"set":[52],"new":[54],"formulations":[55],"Lyapunov-like":[57],"lemmas":[58],"are":[64],"established.":[65],"Finally,":[66],"an":[67],"example":[68],"presented":[70],"verify":[72],"theoretical":[74],"results":[75],"in":[76],"this":[77],"paper.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2017-07-14T00:00:00"}