{"id":"https://openalex.org/W2758120063","doi":"https://doi.org/10.1109/jas.2017.7510646","title":"Numerical solution of the distributed-order fractional Bagley-Torvik equation","display_name":"Numerical solution of the distributed-order fractional Bagley-Torvik equation","publication_year":2017,"publication_date":"2017-09-26","ids":{"openalex":"https://openalex.org/W2758120063","doi":"https://doi.org/10.1109/jas.2017.7510646","mag":"2758120063"},"language":"en","primary_location":{"id":"doi:10.1109/jas.2017.7510646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jas.2017.7510646","pdf_url":null,"source":{"id":"https://openalex.org/S2484288132","display_name":"IEEE/CAA Journal of Automatica Sinica","issn_l":"2329-9266","issn":["2329-9266","2329-9274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE/CAA Journal of Automatica Sinica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027944216","display_name":"Hossein Aminikhah","orcid":"https://orcid.org/0000-0002-2378-5782"},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hossein Aminikhah","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht 41938-19141, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht 41938-19141, Iran","institution_ids":["https://openalex.org/I877176835"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067977581","display_name":"A. H. Refahi Sheikhani","orcid":"https://orcid.org/0000-0003-1664-5471"},"institutions":[{"id":"https://openalex.org/I33162209","display_name":"Islamic Azad University, Lahijan Branch","ror":"https://ror.org/03dhqyc75","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I33162209"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Amir Hosein Refahi Sheikhani","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, Lahijan 1616, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, Lahijan 1616, Iran","institution_ids":["https://openalex.org/I33162209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015023369","display_name":"Tahereh Houlari","orcid":null},"institutions":[{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Tahereh Houlari","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht 41938-19141, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht 41938-19141, Iran","institution_ids":["https://openalex.org/I877176835"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068912075","display_name":"Hadi Rezazadeh","orcid":"https://orcid.org/0000-0003-3800-8406"},"institutions":[{"id":"https://openalex.org/I4210125640","display_name":"Amol University of Special Modern Technologies","ror":"https://ror.org/02twggb97","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210125640"]},{"id":"https://openalex.org/I877176835","display_name":"University of Guilan","ror":"https://ror.org/01bdr6121","country_code":"IR","type":"education","lineage":["https://openalex.org/I877176835"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hadi Rezazadeh","raw_affiliation_strings":["Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol 46168-49767, Iran, and also with the Department of Applied Mathematics, University of Guilan, Rasht 41938-19141, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol 46168-49767, Iran, and also with the Department of Applied Mathematics, University of Guilan, Rasht 41938-19141, Iran","institution_ids":["https://openalex.org/I4210125640","https://openalex.org/I877176835"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9661,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.75034941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"3","first_page":"760","last_page":"765"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6529715061187744},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.5625811219215393},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5252354145050049},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4896436333656311},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48515328764915466},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4506743252277374},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44637003540992737},{"id":"https://openalex.org/keywords/newtonian-fluid","display_name":"Newtonian fluid","score":0.4438358247280121},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14442592859268188},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13382190465927124}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6529715061187744},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.5625811219215393},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5252354145050049},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4896436333656311},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48515328764915466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4506743252277374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44637003540992737},{"id":"https://openalex.org/C294558","wikidata":"https://www.wikidata.org/wiki/Q366968","display_name":"Newtonian fluid","level":2,"score":0.4438358247280121},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14442592859268188},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13382190465927124},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jas.2017.7510646","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jas.2017.7510646","pdf_url":null,"source":{"id":"https://openalex.org/S2484288132","display_name":"IEEE/CAA Journal of Automatica Sinica","issn_l":"2329-9266","issn":["2329-9266","2329-9274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE/CAA Journal of Automatica Sinica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W200132056","https://openalex.org/W1584611818","https://openalex.org/W1989021477","https://openalex.org/W2032772553","https://openalex.org/W2050533316","https://openalex.org/W2072789018","https://openalex.org/W2083559699","https://openalex.org/W2090239694","https://openalex.org/W2093651704","https://openalex.org/W2125677837","https://openalex.org/W2129964093","https://openalex.org/W2134837756","https://openalex.org/W2152152827","https://openalex.org/W2787959293"],"related_works":["https://openalex.org/W3214346900","https://openalex.org/W2978550247","https://openalex.org/W2356099978","https://openalex.org/W2068618939","https://openalex.org/W1992885401","https://openalex.org/W4302011354","https://openalex.org/W3005550969","https://openalex.org/W1989507524","https://openalex.org/W2040224833","https://openalex.org/W191904733"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"two":[3],"numerical":[4],"methods":[5],"are":[6],"proposed":[7],"for":[8],"solving":[9],"distributed-order":[10,44],"fractional":[11,65],"Bagley-Torvik":[12,45],"equation.":[13],"This":[14],"equation":[15,46],"is":[16,47,55],"used":[17],"in":[18,27],"modeling":[19],"the":[20,34,39,43,59,64,76,84,88,92],"motion":[21],"of":[22,79],"a":[23,28,50],"rigid":[24],"plate":[25],"immersed":[26],"Newtonian":[29],"fluid":[30],"with":[31,75],"respect":[32],"to":[33],"nonnegative":[35],"density":[36],"function.":[37],"Using":[38],"composite":[40],"Boole's":[41],"rule":[42],"approximated":[48],"by":[49,58],"multi-term":[51],"time-fractional":[52],"equation,":[53],"which":[54],"then":[56],"solved":[57],"Grunwald-Letnikov":[60],"method":[61,68],"(GLM)":[62],"and":[63,82,91],"differential":[66],"transform":[67],"(FDTM).":[69],"Finally,":[70],"we":[71],"compared":[72],"our":[73],"results":[74,78],"exact":[77,93],"some":[80],"cases":[81],"show":[83],"excellent":[85],"agreement":[86],"between":[87],"approximate":[89],"result":[90],"solution.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
