{"id":"https://openalex.org/W2149285711","doi":"https://doi.org/10.1109/cdc.2012.6426436","title":"Fractional order differentiation by integration with Jacobi polynomials","display_name":"Fractional order differentiation by integration with Jacobi polynomials","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2149285711","doi":"https://doi.org/10.1109/cdc.2012.6426436","mag":"2149285711"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2012.6426436","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426436","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1209.1192","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015407151","display_name":"Da\u2010Yan Liu","orcid":"https://orcid.org/0000-0003-2853-0129"},"institutions":[{"id":"https://openalex.org/I88761825","display_name":"Korea University of Science and Technology","ror":"https://ror.org/000qzf213","country_code":"KR","type":"education","lineage":["https://openalex.org/I88761825"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Da-Yan Liu","raw_affiliation_strings":["Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, South Korea","institution_ids":["https://openalex.org/I88761825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065875611","display_name":"Olivier Gibaru","orcid":"https://orcid.org/0000-0003-1270-6847"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210138412","display_name":"Centre de recherche Inria Lille - Nord Europe","ror":"https://ror.org/04eej9726","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210138412"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Gibaru","raw_affiliation_strings":["L \u00c9quipe Projet Non-A, INRIA Lille-Nord Europe Research Centre, Villeneuve d'Ascq, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L \u00c9quipe Projet Non-A, INRIA Lille-Nord Europe Research Centre, Villeneuve d'Ascq, France","institution_ids":["https://openalex.org/I4210138412","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050319144","display_name":"Wilfrid Perruquetti","orcid":"https://orcid.org/0000-0001-5323-4896"},"institutions":[{"id":"https://openalex.org/I4210138412","display_name":"Centre de recherche Inria Lille - Nord Europe","ror":"https://ror.org/04eej9726","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210138412"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210143894","display_name":"Laboratoire d'Automatique, G\u00e9nie Informatique et Signal","ror":"https://ror.org/04wez4p43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210131494","https://openalex.org/I4210137101","https://openalex.org/I4210139971","https://openalex.org/I4210143894","https://openalex.org/I7454413"]},{"id":"https://openalex.org/I7454413","display_name":"\u00c9cole Centrale de Lille","ror":"https://ror.org/01x441g73","country_code":"FR","type":"education","lineage":["https://openalex.org/I7454413"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wilfrid Perruquetti","raw_affiliation_strings":["L \u00c9quipe Projet Non-A, INRIA Lille-Nord Europe Research Centre, Villeneuve d'Ascq, France","LAGIS (CNRS, UMR 8146), \u00c9cole Centrale de Lille, Villeneuve d'Ascq, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L \u00c9quipe Projet Non-A, INRIA Lille-Nord Europe Research Centre, Villeneuve d'Ascq, France","institution_ids":["https://openalex.org/I4210138412","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"LAGIS (CNRS, UMR 8146), \u00c9cole Centrale de Lille, Villeneuve d'Ascq, France","institution_ids":["https://openalex.org/I7454413","https://openalex.org/I4210143894","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075679869","display_name":"Taous\u2010Meriem Laleg\u2010Kirati","orcid":"https://orcid.org/0000-0001-5944-0121"},"institutions":[{"id":"https://openalex.org/I88761825","display_name":"Korea University of Science and Technology","ror":"https://ror.org/000qzf213","country_code":"KR","type":"education","lineage":["https://openalex.org/I88761825"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Taous-Meriem Laleg-Kirati","raw_affiliation_strings":["Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, South Korea","institution_ids":["https://openalex.org/I88761825"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015407151"],"corresponding_institution_ids":["https://openalex.org/I88761825"],"apc_list":null,"apc_paid":null,"fwci":6.8205,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.96652678,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"10","issue":null,"first_page":"624","last_page":"629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998000264167786,"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":0.9998000264167786,"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/T11236","display_name":"Control Systems and Identification","score":0.9912999868392944,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9818000197410583,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiator","display_name":"Differentiator","score":0.9678747653961182},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.6623367667198181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6333721876144409},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6142475605010986},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6067371964454651},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5378848910331726},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5283421277999878},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.47603586316108704},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41728726029396057},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3134719133377075},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.2966938614845276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2834644019603729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20999732613563538}],"concepts":[{"id":"https://openalex.org/C12112733","wikidata":"https://www.wikidata.org/wiki/Q2659948","display_name":"Differentiator","level":3,"score":0.9678747653961182},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.6623367667198181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6333721876144409},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6142475605010986},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6067371964454651},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5378848910331726},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5283421277999878},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.47603586316108704},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41728726029396057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3134719133377075},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2966938614845276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2834644019603729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20999732613563538},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc.2012.6426436","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6426436","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1209.1192","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.1192","pdf_url":"https://arxiv.org/pdf/1209.1192","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1209.1192","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1209.1192","pdf_url":"https://arxiv.org/pdf/1209.1192","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/565864","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/565864","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1209.1192","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1209.1192","pdf_url":"https://arxiv.org/pdf/1209.1192","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W55790716","https://openalex.org/W1483976166","https://openalex.org/W1511366279","https://openalex.org/W1520195103","https://openalex.org/W1967037921","https://openalex.org/W1978452202","https://openalex.org/W1980361562","https://openalex.org/W1984215648","https://openalex.org/W1985565201","https://openalex.org/W1999913367","https://openalex.org/W2031096349","https://openalex.org/W2032282437","https://openalex.org/W2044183524","https://openalex.org/W2051408351","https://openalex.org/W2064835439","https://openalex.org/W2087747235","https://openalex.org/W2095817904","https://openalex.org/W2102633962","https://openalex.org/W2102756005","https://openalex.org/W2102842504","https://openalex.org/W2103917488","https://openalex.org/W2105646987","https://openalex.org/W2109606373","https://openalex.org/W2117969169","https://openalex.org/W2120062331","https://openalex.org/W2120401159","https://openalex.org/W2131796279","https://openalex.org/W2132686062","https://openalex.org/W2133182476","https://openalex.org/W2134573036","https://openalex.org/W2147692038","https://openalex.org/W2150823344","https://openalex.org/W2155572235","https://openalex.org/W2161411167","https://openalex.org/W2171077359","https://openalex.org/W2623692599","https://openalex.org/W2787959293","https://openalex.org/W2798788284","https://openalex.org/W2962965389","https://openalex.org/W6629059939","https://openalex.org/W6630371737","https://openalex.org/W6658275694","https://openalex.org/W6679672904","https://openalex.org/W6738970532","https://openalex.org/W6910934018"],"related_works":["https://openalex.org/W2353026275","https://openalex.org/W4297612202","https://openalex.org/W2099676275","https://openalex.org/W2949498383","https://openalex.org/W2015514644","https://openalex.org/W4294834596","https://openalex.org/W2493096353","https://openalex.org/W1652500118","https://openalex.org/W1651872008","https://openalex.org/W2793709684"],"abstract_inverted_index":{"The":[0,40,97],"differentiation":[1],"by":[2,11],"integration":[3],"method":[4,22],"with":[5,124],"Jacobi":[6,49,74],"polynomials":[7,75],"was":[8],"originally":[9],"introduced":[10,105],"Mboup,":[12],"Join":[13],"and":[14,53,61,76,94,102,122],"Fliess":[15],"[22],":[16],"[23].":[17],"This":[18],"paper":[19],"generalizes":[20],"this":[21,65],"from":[23,47],"the":[24,28,33,48,54,77,103],"integer":[25],"order":[26,30,35,43,57,108],"to":[27,118,126],"fractional":[29,34,42,56,107],"for":[31,64,92],"estimating":[32],"derivatives":[36],"of":[37],"noisy":[38,78],"signals.":[39],"proposed":[41],"differentiator":[44,66,101,110],"is":[45,67,80,111],"deduced":[46],"orthogonal":[50],"polynomial":[51],"filter":[52],"Riemann-Liouville":[55],"derivative":[58],"definition.":[59],"Exact":[60],"simple":[62],"formula":[63,72],"given":[68,112],"where":[69],"an":[70],"integral":[71],"involving":[73],"signal":[79],"used":[81,90],"without":[82],"complex":[83],"mathematical":[84],"deduction.":[85],"Hence,":[86],"it":[87],"can":[88],"be":[89],"both":[91],"continuous-time":[93],"discrete-time":[95],"models.":[96],"comparison":[98],"between":[99],"our":[100],"recently":[104],"digital":[106],"Savitzky-Golay":[109],"in":[113],"numerical":[114],"simulations":[115],"so":[116],"as":[117],"show":[119],"its":[120],"accuracy":[121],"robustness":[123],"respect":[125],"corrupting":[127],"noises.":[128]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
