{"id":"https://openalex.org/W7128585969","doi":"https://doi.org/10.1007/s00500-026-11183-4","title":"Analysis of solutions of fuzzy differential equations under the generalized derivative","display_name":"Analysis of solutions of fuzzy differential equations under the generalized derivative","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128585969","doi":"https://doi.org/10.1007/s00500-026-11183-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-026-11183-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-026-11183-4","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s00500-026-11183-4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001888085","display_name":"Felipe Longo","orcid":"https://orcid.org/0000-0002-2868-3937"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Felipe Longo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036304475","display_name":"Beatriz Laiate","orcid":"https://orcid.org/0000-0002-7312-4843"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beatriz Laiate","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125618707","display_name":"Marta C. Gadotti","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marta C. Gadotti","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125605089","display_name":"Jo\u00e3o F. C. A. Meyer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jo\u00e3o F. C. A. Meyer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001888085"],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34315068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"4","first_page":"2219","last_page":"2237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.006300000008195639,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0027000000700354576,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.631600022315979},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.46959999203681946},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.44350001215934753},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.42489999532699585},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.41440001130104065},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.40049999952316284},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3882000148296356},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.3555000126361847},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.34779998660087585}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165000081062317},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.631600022315979},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47940000891685486},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.46959999203681946},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.44350001215934753},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.41440001130104065},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.40049999952316284},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.34779998660087585},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.34529998898506165},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.34150001406669617},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.34119999408721924},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.3352000117301941},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3346000015735626},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.3228999972343445},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.31380000710487366},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31189998984336853},{"id":"https://openalex.org/C180802074","wikidata":"https://www.wikidata.org/wiki/Q1052379","display_name":"Logistic function","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C184537036","wikidata":"https://www.wikidata.org/wiki/Q14163503","display_name":"Generalizations of the derivative","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2745000123977661},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-026-11183-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-026-11183-4","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"Soft Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00500-026-11183-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00500-026-11183-4","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"Soft Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323854","display_name":"Universidade Estadual de Campinas","ror":"https://ror.org/04wffgt70"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W565587792","https://openalex.org/W1549251788","https://openalex.org/W1680454679","https://openalex.org/W1928951487","https://openalex.org/W1965955764","https://openalex.org/W1979756370","https://openalex.org/W1982606567","https://openalex.org/W1994178762","https://openalex.org/W1995123739","https://openalex.org/W2006127887","https://openalex.org/W2013367574","https://openalex.org/W2017586937","https://openalex.org/W2034038007","https://openalex.org/W2038354216","https://openalex.org/W2070545443","https://openalex.org/W2076628063","https://openalex.org/W2083742942","https://openalex.org/W2092628318","https://openalex.org/W2162836710","https://openalex.org/W2336761277","https://openalex.org/W2580890888","https://openalex.org/W2885266427","https://openalex.org/W3116849867","https://openalex.org/W3169174001","https://openalex.org/W3207674875","https://openalex.org/W4239193822","https://openalex.org/W4386826982","https://openalex.org/W4387614395","https://openalex.org/W4393009464","https://openalex.org/W4393233977"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1,84],"generalized":[2,31],"derivative":[3,11],"represents":[4],"the":[5,9,18,30,50,60,93,99,111,120,125,159,171],"broadest":[6],"notion":[7],"of":[8,12,26,37,54,77,92,96,104,113,124,137,154],"Hukuhara-type":[10,72],"a":[13,23,70,89,105,114],"fuzzy":[14,27,38,66,106,115,132],"number-valued":[15],"function":[16],"in":[17],"literature.":[19],"It":[20],"exists":[21,33],"for":[22,34,119,170],"wide":[24],"class":[25],"processes,":[28],"since":[29],"difference":[32],"any":[35],"pair":[36],"numbers.":[39],"Despite":[40],"its":[41,55],"historical":[42],"significance,":[43],"few":[44],"papers":[45],"provide":[46],"theoretical":[47],"results":[48,130],"on":[49,131],"g-derivative,":[51],"primarily":[52],"because":[53],"complex":[56],"analytical":[57],"behavior.":[58],"On":[59],"other":[61],"hand,":[62],"analyzing":[63],"solutions":[64,80,126,136],"to":[65,166],"differential":[67],"equations":[68],"from":[69,135],"comparative":[71],"perspective":[73],"allows":[74],"establishing":[75],"features":[76],"FDEs":[78,138],"whose":[79],"are":[81,127,140,151,164],"exclusively":[82],"g-differentiable.":[83],"study":[85],"begins":[86],"by":[87,158],"providing":[88],"corrected":[90],"version":[91],"fundamental":[94],"theorem":[95],"calculus":[97],"via":[98],"g-differentiability":[100],"and":[101,145,161],"Aumann":[102],"integrability":[103],"function.":[107],"Sufficient":[108],"conditions":[109],"over":[110],"field":[112],"initial":[116],"value":[117],"problem":[118],"gH":[121,148],"$$*$$":[122,149],"-differentiability":[123],"presented.":[128],"Lastly,":[129],"processes":[133],"derived":[134],"that":[139],"g-differentiable,":[141],"but":[142],"not":[143,146],"gH,":[144],"even":[147],"-differentiable,":[150],"given.":[152],"Examples":[153],"population":[155],"dynamics":[156],"governed":[157],"Malthusian":[160],"Logistic":[162],"models":[163],"provided":[165],"illustrate":[167],"different":[168],"scenarios":[169],"presented":[172],"analysis.":[173]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2026-02-11T00:00:00"}