{"id":"https://openalex.org/W4280505391","doi":"https://doi.org/10.3390/axioms11050231","title":"Taylor\u2019s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels","display_name":"Taylor\u2019s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels","publication_year":2022,"publication_date":"2022-05-15","ids":{"openalex":"https://openalex.org/W4280505391","doi":"https://doi.org/10.3390/axioms11050231"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050231","pdf_url":"https://www.mdpi.com/2075-1680/11/5/231/pdf?version=1652621277","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/5/231/pdf?version=1652621277","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003920258","display_name":"Houssine Zine","orcid":"https://orcid.org/0000-0002-8412-7783"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Houssine Zine","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051424822","display_name":"El Mehdi Lotfi","orcid":"https://orcid.org/0000-0002-3604-3841"},"institutions":[{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"El Mehdi Lotfi","raw_affiliation_strings":["Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco"],"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]},{"raw_affiliation_string":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057131265","display_name":"Delfim F. M. Torres","orcid":"https://orcid.org/0000-0001-8641-2505"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Delfim F. M. Torres","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090815657","display_name":"Noura Yousfi","orcid":"https://orcid.org/0000-0001-8435-5981"},"institutions":[{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Noura Yousfi","raw_affiliation_strings":["Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco"],"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]},{"raw_affiliation_string":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057131265"],"corresponding_institution_ids":["https://openalex.org/I60858718"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8117,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.6625989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"11","issue":"5","first_page":"231","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/invertible-matrix","display_name":"Invertible matrix","score":0.9158815145492554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8463382720947266},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7083759307861328},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.6145385503768921},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47097277641296387},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4601377546787262},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.42433348298072815},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36218392848968506},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27806341648101807},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07697051763534546}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.9158815145492554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8463382720947266},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7083759307861328},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.6145385503768921},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47097277641296387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4601377546787262},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.42433348298072815},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36218392848968506},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27806341648101807},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07697051763534546},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11050231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050231","pdf_url":"https://www.mdpi.com/2075-1680/11/5/231/pdf?version=1652621277","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:143675f1033c4e85b80e2cec12c37b81","is_oa":true,"landing_page_url":"https://doaj.org/article/143675f1033c4e85b80e2cec12c37b81","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 5, p 231 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/231/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050231","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms; Volume 11; Issue 5; Pages: 231","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050231","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050231","pdf_url":"https://www.mdpi.com/2075-1680/11/5/231/pdf?version=1652621277","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2867470761","display_name":null,"funder_award_id":"UIDB/04106/2020 (CIDMA)","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280505391.pdf","grobid_xml":"https://content.openalex.org/works/W4280505391.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W260145074","https://openalex.org/W1968820480","https://openalex.org/W1989638117","https://openalex.org/W2001318028","https://openalex.org/W2007735580","https://openalex.org/W2040469847","https://openalex.org/W2056442151","https://openalex.org/W2057414857","https://openalex.org/W2086472217","https://openalex.org/W2088397042","https://openalex.org/W2093056734","https://openalex.org/W2556784265","https://openalex.org/W2604697252","https://openalex.org/W2624991620","https://openalex.org/W2763368435","https://openalex.org/W2773389758","https://openalex.org/W2792479230","https://openalex.org/W2902351808","https://openalex.org/W2963641381","https://openalex.org/W2977046017","https://openalex.org/W3027645126","https://openalex.org/W3029985551","https://openalex.org/W3030631368","https://openalex.org/W3030688976","https://openalex.org/W3084134122","https://openalex.org/W3109634920","https://openalex.org/W3125824559","https://openalex.org/W3137152733","https://openalex.org/W3153183877","https://openalex.org/W3164248124","https://openalex.org/W3164746976","https://openalex.org/W3175478594","https://openalex.org/W3178628201","https://openalex.org/W3184826897","https://openalex.org/W3185181261","https://openalex.org/W3185820607","https://openalex.org/W3186825494","https://openalex.org/W3187425863","https://openalex.org/W3192570559","https://openalex.org/W3201979259","https://openalex.org/W4214693015","https://openalex.org/W4300962917","https://openalex.org/W6660479309","https://openalex.org/W6665028510","https://openalex.org/W6730176618","https://openalex.org/W6736120499","https://openalex.org/W6798297574","https://openalex.org/W6799100701","https://openalex.org/W6799101207"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W2784467519","https://openalex.org/W4289867043","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2350707375","https://openalex.org/W2377881809","https://openalex.org/W2355516922","https://openalex.org/W1537973975","https://openalex.org/W4312960772"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2],"new":[3,22,34],"Taylor\u2019s":[4,53],"theorem":[5],"for":[6,24,38,58],"generalized":[7,26,39],"weighted":[8,40,63],"fractional":[9,27,41],"calculus":[10],"with":[11],"nonsingular":[12],"kernels.":[13],"The":[14],"proof":[15],"is":[16],"based":[17],"on":[18],"the":[19,51],"establishment":[20],"of":[21],"relations":[23],"nth-weighted":[25],"integrals":[28],"and":[29,54,62],"derivatives.":[30,65],"As":[31],"an":[32],"application,":[33],"mean":[35,55],"value":[36,56],"theorems":[37,57],"operators":[42],"are":[43],"obtained.":[44],"Direct":[45],"corollaries":[46],"allow":[47],"one":[48],"to":[49],"obtain":[50],"recent":[52],"Caputo\u2013Fabrizio,":[59],"Atangana\u2013Baleanu\u2013Caputo":[60],"(ABC)":[61],"ABC":[64]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}