{"id":"https://openalex.org/W3203202756","doi":"https://doi.org/10.5455/sf.93078","title":"Solution of Linear Ordinary Differential Equations in Fuzzy Environment by Method of Variation of Parameters","display_name":"Solution of Linear Ordinary Differential Equations in Fuzzy Environment by Method of Variation of Parameters","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3203202756","doi":"https://doi.org/10.5455/sf.93078","mag":"3203202756"},"language":"en","primary_location":{"id":"doi:10.5455/sf.93078","doi":"https://doi.org/10.5455/sf.93078","is_oa":false,"landing_page_url":"https://doi.org/10.5455/sf.93078","pdf_url":null,"source":{"id":"https://openalex.org/S4210210550","display_name":"Science Forum (Journal of Pure and Applied Sciences)","issn_l":"1119-4618","issn":["1119-4618"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science Forum (Journal of Pure and Applied Sciences)","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://atbuscienceforum.com.ng/index.php/jpas/article/download/427/431","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022691634","display_name":"Udot Asuquo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Udot Asuquo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111094704","display_name":"Alhaji Tahir","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alhaji Tahir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040734669","display_name":"U. Sulaiman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Usman Sulaiman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111094704","display_name":"Alhaji Tahir","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alhaji Tahir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"3","first_page":"583","last_page":"583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":1.0,"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":1.0,"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":0.0,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-valued-functions","display_name":"fuzzy-valued functions","score":0.8560000061988831},{"id":"https://openalex.org/keywords/variation-of-parameters","display_name":"variation of parameters","score":0.9710000157356262},{"id":"https://openalex.org/keywords/linear-ordinary-differential-equations","display_name":"linear ordinary differential equations","score":0.6959999799728394},{"id":"https://openalex.org/keywords/fuzzy-differential-equations","display_name":"fuzzy differential equations","score":0.8080000281333923}],"concepts":[{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6700805425643921},{"id":"https://openalex.org/C62689967","wikidata":"https://www.wikidata.org/wiki/Q1205942","display_name":"Variation of parameters","level":3,"score":0.6584206819534302},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.6420658826828003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5884175896644592},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.551192045211792},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4715540409088135},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.457547128200531},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31904351711273193},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31812095642089844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19694259762763977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15304240584373474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.043677061796188354},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5455/sf.93078","doi":"https://doi.org/10.5455/sf.93078","is_oa":false,"landing_page_url":"https://doi.org/10.5455/sf.93078","pdf_url":null,"source":{"id":"https://openalex.org/S4210210550","display_name":"Science Forum (Journal of Pure and Applied Sciences)","issn_l":"1119-4618","issn":["1119-4618"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Science Forum (Journal of Pure and Applied Sciences)","raw_type":"journal-article"},{"id":"pmh:oai:ojs2.atbuscienceforum.com.ng:article/427","doi":null,"is_oa":true,"landing_page_url":"https://atbuscienceforum.com.ng/index.php/jpas/article/view/427","pdf_url":"https://atbuscienceforum.com.ng/index.php/jpas/article/download/427/431","source":{"id":"https://openalex.org/S4210210550","display_name":"Science Forum (Journal of Pure and Applied Sciences)","issn_l":"1119-4618","issn":["1119-4618"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1119-4618","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ojs2.atbuscienceforum.com.ng:article/427","doi":null,"is_oa":true,"landing_page_url":"https://atbuscienceforum.com.ng/index.php/jpas/article/view/427","pdf_url":"https://atbuscienceforum.com.ng/index.php/jpas/article/download/427/431","source":{"id":"https://openalex.org/S4210210550","display_name":"Science Forum (Journal of Pure and Applied Sciences)","issn_l":"1119-4618","issn":["1119-4618"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1119-4618","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3203202756.pdf","grobid_xml":"https://content.openalex.org/works/W3203202756.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2038354216","https://openalex.org/W2103090030","https://openalex.org/W2363817003"],"related_works":["https://openalex.org/W3084108296","https://openalex.org/W2388678205","https://openalex.org/W4386119327","https://openalex.org/W3212058989","https://openalex.org/W2043201461","https://openalex.org/W7168098000","https://openalex.org/W2152054466","https://openalex.org/W2510454860","https://openalex.org/W3216164525","https://openalex.org/W4205789873"],"abstract_inverted_index":{"This":[0],"work":[1],"considers":[2],"linear":[3],"fuzzy":[4,35],"initial":[5],"value":[6],"problems":[7],"(LFIVPs)":[8],"defined":[9],"under":[10],"gH-differentiability":[11,41,49],"with":[12],"the":[13,29,88,91,96,101],"aim":[14],"of":[15,70,75,77,90,95,98,100,109],"establishing":[16],"a":[17,21,26,34,68],"method":[18,74],"and,":[19],"subsequently,":[20],"fuzzy-valued":[22,52],"function,":[23],"which":[24],"is":[25,54,79,104],"solution":[27],"to":[28,37,51,65,86],"LFIVPs.":[30,82,126],"The":[31,73],"conditions":[32],"for":[33],"function":[36],"be":[38,119],"Hukuharanbsp;(H)-differentiable":[39],"and":[40,59,93,123],"are":[42,62,84],"defined.":[43],"It":[44],"is,":[45],"however,":[46],"established":[47],"thatnbsp;the":[48],"concept":[50],"functions":[53],"more":[55],"generalized":[56],"thannbsp;H-differentiable.":[57],"Characterization":[58],"stacking":[60],"theorems":[61],"also":[63,80],"used":[64],"translate":[66],"LFIVPsnbsp;to":[67],"system":[69],"specialized":[71],"ODEs.":[72],"variation":[76],"parameters":[78],"extendednbsp;to":[81],"Examples":[83],"constructed":[85,102],"test":[87],"applicability":[89],"methods":[92],"graphicalnbsp;presentation":[94],"behavior":[97],"solutions":[99],"examples":[103],"carried":[105,120],"out":[106],"withnbsp;the":[107],"aid":[108],"MATLAB":[110],"version":[111],"8.5.":[112],"We":[113],"recommend":[114],"that":[115],"further":[116],"studies":[117],"should":[118],"outnbsp;on":[121],"second":[122],"higher":[124],"order":[125]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2021-10-11T00:00:00"}