{"id":"https://openalex.org/W2525291455","doi":"https://doi.org/10.1515/amcs-2016-0037","title":"Fractional descriptor continuous\u2013time linear systems described by the Caputo\u2013Fabrizio derivative","display_name":"Fractional descriptor continuous\u2013time linear systems described by the Caputo\u2013Fabrizio derivative","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2525291455","doi":"https://doi.org/10.1515/amcs-2016-0037","mag":"2525291455"},"language":"en","primary_location":{"id":"doi:10.1515/amcs-2016-0037","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2016-0037","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/3/article-p533.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/3/article-p533.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081405480","display_name":"Tadeusz Kaczorek","orcid":"https://orcid.org/0000-0002-1270-3948"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Tadeusz Kaczorek","raw_affiliation_strings":["Faculty of Electrical Engineering, Bia\u0142ystok Technical University, Wiejska 45D, 15-351 Bia\u0142ystok, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Bia\u0142ystok Technical University, Wiejska 45D, 15-351 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084024155","display_name":"Kamil Borawski","orcid":"https://orcid.org/0000-0001-7325-1159"},"institutions":[{"id":"https://openalex.org/I1323121030","display_name":"Bialystok University of Technology","ror":"https://ror.org/02bzfsy61","country_code":"PL","type":"education","lineage":["https://openalex.org/I1323121030"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Kamil Borawski","raw_affiliation_strings":["Faculty of Electrical Engineering, Bia\u0142ystok Technical University, Wiejska 45D, 15-351 Bia\u0142ystok, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Bia\u0142ystok Technical University, Wiejska 45D, 15-351 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I1323121030"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081405480"],"corresponding_institution_ids":["https://openalex.org/I1323121030"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":4.5891,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94868386,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"26","issue":"3","first_page":"533","last_page":"541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9950000047683716,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9950000047683716,"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":0.9940000176429749,"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":0.9934999942779541,"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/kronecker-delta","display_name":"Kronecker delta","score":0.8214040994644165},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.7564468383789062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7016573548316956},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5956923961639404},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.534065306186676},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5183823704719543},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4910252094268799},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.472858190536499},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4609193801879883},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.460050106048584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31341731548309326},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19981041550636292}],"concepts":[{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.8214040994644165},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.7564468383789062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7016573548316956},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5956923961639404},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.534065306186676},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5183823704719543},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4910252094268799},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.472858190536499},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4609193801879883},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.460050106048584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31341731548309326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19981041550636292},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/amcs-2016-0037","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2016-0037","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/3/article-p533.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:784a3f4736424de98c3c91de05abcd7a","is_oa":true,"landing_page_url":"https://doaj.org/article/784a3f4736424de98c3c91de05abcd7a","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science, Vol 26, Iss 3, Pp 533-541 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/amcs-2016-0037","is_oa":true,"landing_page_url":"https://doi.org/10.1515/amcs-2016-0037","pdf_url":"https://content.sciendo.com/downloadpdf/journals/amcs/26/3/article-p533.pdf","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2525291455.pdf","grobid_xml":"https://content.openalex.org/works/W2525291455.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W151868298","https://openalex.org/W153570590","https://openalex.org/W578411849","https://openalex.org/W655150127","https://openalex.org/W1518580955","https://openalex.org/W1534430411","https://openalex.org/W1588609682","https://openalex.org/W1604304367","https://openalex.org/W1982840747","https://openalex.org/W1991090448","https://openalex.org/W2000470692","https://openalex.org/W2003580237","https://openalex.org/W2016031226","https://openalex.org/W2076911229","https://openalex.org/W2078307864","https://openalex.org/W2097178696","https://openalex.org/W2118039425","https://openalex.org/W2128978199","https://openalex.org/W2139207988","https://openalex.org/W2141576184","https://openalex.org/W2187932833","https://openalex.org/W2516163476","https://openalex.org/W2556784265","https://openalex.org/W2688139507","https://openalex.org/W4235143360","https://openalex.org/W4247285924","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2770308590","https://openalex.org/W2097178696","https://openalex.org/W2128217535","https://openalex.org/W2095223301","https://openalex.org/W2016208021","https://openalex.org/W1996288653","https://openalex.org/W1751457437","https://openalex.org/W2091170701","https://openalex.org/W2166068341","https://openalex.org/W2303805716"],"abstract_inverted_index":{"Abstract":[0],"The":[1,48],"Weierstrass\u2013Kronecker":[2],"theorem":[3],"on":[4],"the":[5,8,21,39],"decomposition":[6],"of":[7,29,43],"regular":[9],"pencil":[10],"is":[11,32,50],"extended":[12],"to":[13],"fractional":[14],"descriptor":[15],"continuous-time":[16,30],"linear":[17],"systems":[18,31,45],"described":[19],"by":[20],"Caputo\u2013Fabrizio":[22],"derivative.":[23],"A":[24],"method":[25],"for":[26,38],"computing":[27],"solutions":[28],"presented.":[33],"Necessary":[34],"and":[35,41],"sufficient":[36],"conditions":[37],"positivity":[40],"stability":[42],"these":[44],"are":[46],"established.":[47],"discussion":[49],"illustrated":[51],"with":[52],"a":[53],"numerical":[54],"example.":[55]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2016-10-07T00:00:00"}