{"id":"https://openalex.org/W4409674750","doi":"https://doi.org/10.1007/s40314-025-03209-8","title":"On partial Caputo fractional models","display_name":"On partial Caputo fractional models","publication_year":2025,"publication_date":"2025-04-22","ids":{"openalex":"https://openalex.org/W4409674750","doi":"https://doi.org/10.1007/s40314-025-03209-8"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03209-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03209-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03209-8.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03209-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107678055","display_name":"Julia Calatayud","orcid":"https://orcid.org/0000-0002-9639-1530"},"institutions":[{"id":"https://openalex.org/I10902133","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11","country_code":"ES","type":"education","lineage":["https://openalex.org/I10902133"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Julia Calatayud","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Jaume I, 12071, Castell\u00f3n de la Plana, Castell\u00f3n, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Jaume I, 12071, Castell\u00f3n de la Plana, Castell\u00f3n, Spain","institution_ids":["https://openalex.org/I10902133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005181342","display_name":"Marc Jornet","orcid":"https://orcid.org/0000-0003-0748-3730"},"institutions":[{"id":"https://openalex.org/I4210116615","display_name":"Universidad Internacional De La Rioja","ror":"https://ror.org/029gnnp81","country_code":"ES","type":"education","lineage":["https://openalex.org/I4210116615"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Marc Jornet","raw_affiliation_strings":["Escuela Superior de Ingenier\u00eda y Tecnolog\u00eda, Universidad Internacional de La Rioja, Av. La Paz 137, 26006, Logro\u00f1o, Spain"],"affiliations":[{"raw_affiliation_string":"Escuela Superior de Ingenier\u00eda y Tecnolog\u00eda, Universidad Internacional de La Rioja, Av. La Paz 137, 26006, Logro\u00f1o, Spain","institution_ids":["https://openalex.org/I4210116615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022418028","display_name":"Carla M. A. Pinto","orcid":"https://orcid.org/0000-0002-0729-1133"},"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"]},{"id":"https://openalex.org/I83863532","display_name":"Polytechnic Institute of Porto","ror":"https://ror.org/04988re48","country_code":"PT","type":"education","lineage":["https://openalex.org/I83863532"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Carla M. A. Pinto","raw_affiliation_strings":["Polytechnic of Porto - ISEP, Porto, and CIDMA, University of Aveiro, Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Polytechnic of Porto - ISEP, Porto, and CIDMA, University of Aveiro, Aveiro, Portugal","institution_ids":["https://openalex.org/I83863532","https://openalex.org/I60858718"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107678055"],"corresponding_institution_ids":["https://openalex.org/I10902133"],"apc_list":null,"apc_paid":null,"fwci":2.5942,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87898148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"44","issue":"5","first_page":null,"last_page":null},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9962999820709229,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/applied-mathematics","display_name":"Applied mathematics","score":0.4475998878479004},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4469715654850006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40670090913772583}],"concepts":[{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4475998878479004},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4469715654850006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40670090913772583}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03209-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03209-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03209-8.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s40314-025-03209-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03209-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03209-8.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3272457656","display_name":null,"funder_award_id":"UIDB/","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G5415677114","display_name":null,"funder_award_id":"UIDB/00144/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G8367123964","display_name":null,"funder_award_id":"UIDB/00144/2020","funder_id":"https://openalex.org/F4320335191","funder_display_name":"Centro de Matem\u00e1tica Universidade do Porto"}],"funders":[{"id":"https://openalex.org/F4320322926","display_name":"Universitat Jaume I","ror":"https://ror.org/02ws1xc11"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320335191","display_name":"Centro de Matem\u00e1tica Universidade do Porto","ror":"https://ror.org/043pwc612"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409674750.pdf","grobid_xml":"https://content.openalex.org/works/W4409674750.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W240029891","https://openalex.org/W302752317","https://openalex.org/W860356078","https://openalex.org/W1277962881","https://openalex.org/W1494628843","https://openalex.org/W1803895608","https://openalex.org/W1972658648","https://openalex.org/W1988093952","https://openalex.org/W2013977983","https://openalex.org/W2068762033","https://openalex.org/W2091879618","https://openalex.org/W2121498877","https://openalex.org/W2123227340","https://openalex.org/W2277658786","https://openalex.org/W2911086407","https://openalex.org/W2981830447","https://openalex.org/W3120648879","https://openalex.org/W3128296994","https://openalex.org/W3133982482","https://openalex.org/W3139540749","https://openalex.org/W3143141409","https://openalex.org/W3155816154","https://openalex.org/W3157122663","https://openalex.org/W3157868670","https://openalex.org/W3210138770","https://openalex.org/W4206653987","https://openalex.org/W4236369371","https://openalex.org/W4241819982","https://openalex.org/W4247953052","https://openalex.org/W4313442591","https://openalex.org/W4391162851","https://openalex.org/W4391335278","https://openalex.org/W4392426924","https://openalex.org/W4392888169","https://openalex.org/W4394815446","https://openalex.org/W4399040570","https://openalex.org/W4400642270","https://openalex.org/W4400691544","https://openalex.org/W4401043662"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"partial":[2,148],"Caputo":[3,48,149],"fractional":[4,49,75,101],"model":[5],"mixes,":[6],"in":[7,15],"the":[8,16,30,37,54,61,68,117],"same":[9],"formulation,":[10],"classical":[11],"and":[12,20,28,84,104,106,131,141],"Riemann\u2013Liouville":[13,23],"terms,":[14],"realm":[17],"of":[18,34,46,53,86,112,147],"epidemiology":[19],"sociology.":[21],"The":[22,144],"part":[24],"introduces":[25],"non-Markovian":[26],"behavior":[27],"makes":[29],"hazard":[31],"risk":[32],"function":[33],"transition":[35],"between":[36],"compartments":[38],"lower":[39],"as":[40],"time":[41],"advances.":[42],"As":[43],"a":[44,97],"generalization":[45],"standard":[47],"models,":[50],"where":[51],"all":[52],"terms":[55],"are":[56,78,122],"fractional,":[57],"here":[58],"we":[59],"investigate":[60],"mathematical":[62],"theory":[63],"on":[64,100],"incomplete":[65],"fractionalization.":[66],"Essentially,":[67],"goal":[69],"is":[70,151],"to":[71,90],"prove":[72],"that":[73],"partially":[74],"initial-value":[76],"problems":[77],"well":[79],"posed,":[80],"with":[81,88,116,135,153],"existence,":[82,127],"uniqueness,":[83],"continuity":[85],"solution":[87],"respect":[89],"input":[91],"data.":[92],"We":[93],"present":[94],"fixed-point":[95],"results,":[96],"Cauchy\u2013Kovalevskaya":[98],"theorem":[99],"power":[102],"series,":[103],"Gronwall-":[105],"Nagumo-like":[107],"arguments":[108],"for":[109],"uniqueness.":[110],"Continuity":[111],"solutions":[113,134],"uses":[114],"bounds":[115],"Mittag-Leffler":[118],"function.":[119],"Linear":[120],"equations":[121],"also":[123],"addressed,":[124],"exhibiting":[125],"global":[126,128],"power-series":[129],"representation,":[130],"certain":[132],"closed-form":[133],"Mikusi\u0144ski":[136],"operational":[137],"calculus,":[138],"refined":[139],"bounds,":[140],"stability":[142],"properties.":[143],"stochastic":[145],"counterpart":[146],"models":[150],"introduced,":[152],"several":[154],"results.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}