{"id":"https://openalex.org/W4409097139","doi":"https://doi.org/10.3390/sym17040545","title":"Numerical Solution for Fuzzy Fractional Differential Equations by Fuzzy Multi-Step Methods","display_name":"Numerical Solution for Fuzzy Fractional Differential Equations by Fuzzy Multi-Step Methods","publication_year":2025,"publication_date":"2025-04-02","ids":{"openalex":"https://openalex.org/W4409097139","doi":"https://doi.org/10.3390/sym17040545"},"language":"en","primary_location":{"id":"doi:10.3390/sym17040545","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040545","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym17040545","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054673522","display_name":"Leila Safikhani","orcid":null},"institutions":[{"id":"https://openalex.org/I110525433","display_name":"Islamic Azad University, Tehran","ror":"https://ror.org/01kzn7k21","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Leila Safikhani","raw_affiliation_strings":["Department of Mathematics, Miyaneh Branch Islamic Azad University, Miyaneh 14778-93855, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Miyaneh Branch Islamic Azad University, Miyaneh 14778-93855, Iran","institution_ids":["https://openalex.org/I110525433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073095019","display_name":"Tofigh Allahviranloo","orcid":"https://orcid.org/0000-0002-6673-3560"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]},{"id":"https://openalex.org/I4210121333","display_name":"Istinye University","ror":"https://ror.org/03081nz23","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210121333"]}],"countries":["IR","TR"],"is_corresponding":false,"raw_author_name":"Tofigh Allahviranloo","raw_affiliation_strings":["Quantum Technologies Research Center, Science and Research Branch, Islamic Azad University, Tehran 14778-93855, Iran","Research Center of Performance and Productivity Analysis, Istinye University, Istanbul 34396, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-6673-3560","affiliations":[{"raw_affiliation_string":"Quantum Technologies Research Center, Science and Research Branch, Islamic Azad University, Tehran 14778-93855, Iran","institution_ids":["https://openalex.org/I155419210"]},{"raw_affiliation_string":"Research Center of Performance and Productivity Analysis, Istinye University, Istanbul 34396, T\u00fcrkiye","institution_ids":["https://openalex.org/I4210121333"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021603065","display_name":"Leo Mr\u0161i\u0107","orcid":"https://orcid.org/0000-0002-5093-3453"},"institutions":[{"id":"https://openalex.org/I4210088608","display_name":"Higher Education Centre Novo Mesto","ror":"https://ror.org/00ak23720","country_code":"SI","type":"education","lineage":["https://openalex.org/I4210088608"]},{"id":"https://openalex.org/I4210102288","display_name":"Algebra Bernays University","ror":"https://ror.org/019m6wk21","country_code":"HR","type":"education","lineage":["https://openalex.org/I4210102288"]}],"countries":["HR","SI"],"is_corresponding":false,"raw_author_name":"Leo Mrsic","raw_affiliation_strings":["Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia","Rudolfovo\u2014Science and Technology Centre Novo Mesto, Podbreznik 15, 8000 Novo Mesto, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-5093-3453","affiliations":[{"raw_affiliation_string":"Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia","institution_ids":["https://openalex.org/I4210102288"]},{"raw_affiliation_string":"Rudolfovo\u2014Science and Technology Centre Novo Mesto, Podbreznik 15, 8000 Novo Mesto, Slovenia","institution_ids":["https://openalex.org/I4210088608"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088135807","display_name":"Sovan Samanta","orcid":"https://orcid.org/0000-0003-3200-8990"},"institutions":[{"id":"https://openalex.org/I4210102288","display_name":"Algebra Bernays University","ror":"https://ror.org/019m6wk21","country_code":"HR","type":"education","lineage":["https://openalex.org/I4210102288"]},{"id":"https://openalex.org/I4210121333","display_name":"Istinye University","ror":"https://ror.org/03081nz23","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210121333"]}],"countries":["HR","TR"],"is_corresponding":false,"raw_author_name":"Sovan Samanta","raw_affiliation_strings":["Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk 721636, India","Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia","Research Center of Performance and Productivity Analysis, Istinye University, Istanbul 34396, T\u00fcrkiye"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk 721636, India","institution_ids":[]},{"raw_affiliation_string":"Department of Technical Sciences, Algebra Bernays University, Gradiscanska 24, 10000 Zagreb, Croatia","institution_ids":["https://openalex.org/I4210102288"]},{"raw_affiliation_string":"Research Center of Performance and Productivity Analysis, Istinye University, Istanbul 34396, T\u00fcrkiye","institution_ids":["https://openalex.org/I4210121333"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06826037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"545","last_page":"545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9786999821662903,"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":0.9786999821662903,"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":0.9513999819755554,"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":0.925599992275238,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.6359601616859436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5263025760650635},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4804810583591461},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4460747539997101},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39667627215385437},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2596600651741028},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1093282699584961}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6359601616859436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5263025760650635},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4804810583591461},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4460747539997101},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39667627215385437},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2596600651741028},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1093282699584961}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17040545","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040545","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:dirros.openscience.si:IzpisGradiva.php?id=22651","is_oa":true,"landing_page_url":"https://dirros.openscience.si/IzpisGradiva.php?id=22651","pdf_url":null,"source":{"id":"https://openalex.org/S4377196363","display_name":"DiRROS repository (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 2073-8994","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym17040545","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040545","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","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/W4285308861"],"abstract_inverted_index":{"To":[0,73],"solve":[1],"fractional":[2,65],"differential":[3,32,66],"equations,":[4],"they":[5],"are":[6,110],"typically":[7],"converted":[8],"into":[9],"their":[10],"corresponding":[11],"crisp":[12],"problems":[13],"through":[14],"a":[15,25],"process":[16],"known":[17],"as":[18],"the":[19,38,48,54,75,80,86,91,98,114,119],"embedding":[20],"method.":[21],"This":[22],"paper":[23],"introduces":[24],"novel":[26],"direct":[27],"approach":[28],"to":[29,59,112],"solving":[30],"fuzzy":[31,35,49,55,64,70],"equations":[33,67],"using":[34],"calculations,":[36],"bypassing":[37],"need":[39],"for":[40,63],"this":[41,44],"transformation.":[42],"In":[43],"study,":[45],"we":[46,83,96],"develop":[47],"Adams\u2013Bashforth":[50],"(A-B)":[51],"method":[52,58],"and":[53,77,90,100,116],"Adams\u2013Moulton":[56],"(A-M)":[57],"find":[60],"numerical":[61,108],"solutions":[62],"(FFDEs)":[68],"with":[69],"initial":[71],"values.":[72],"demonstrate":[74],"accuracy":[76],"efficiency":[78],"of":[79,102,118],"proposed":[81,120],"methods,":[82],"determine":[84],"both":[85],"local":[87],"truncation":[88,93],"error":[89],"global":[92],"error.":[94],"Additionally,":[95],"establish":[97],"convergence":[99],"stability":[101],"these":[103],"methods":[104],"in":[105],"detail.":[106],"Finally,":[107],"examples":[109],"provided":[111],"illustrate":[113],"flexibility":[115],"effectiveness":[117],"methods.":[121]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
