{"id":"https://openalex.org/W2058503713","doi":"https://doi.org/10.1080/00207160903474214","title":"Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation","display_name":"Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation","publication_year":2010,"publication_date":"2010-11-28","ids":{"openalex":"https://openalex.org/W2058503713","doi":"https://doi.org/10.1080/00207160903474214","mag":"2058503713"},"language":"en","primary_location":{"id":"doi:10.1080/00207160903474214","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903474214","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5029915868","display_name":"Subir Das","orcid":"https://orcid.org/0000-0002-9540-2883"},"institutions":[{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S. Das","raw_affiliation_strings":["a   Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005,  India","Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005, India"],"affiliations":[{"raw_affiliation_string":"a   Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005,  India","institution_ids":["https://openalex.org/I91357014"]},{"raw_affiliation_string":"Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005, India","institution_ids":["https://openalex.org/I91357014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100675978","display_name":"Praveen Kumar Gupta","orcid":"https://orcid.org/0000-0002-0889-9802"},"institutions":[{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"P. K. Gupta","raw_affiliation_strings":["a   Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005,  India","Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005, India"],"affiliations":[{"raw_affiliation_string":"a   Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005,  India","institution_ids":["https://openalex.org/I91357014"]},{"raw_affiliation_string":"Department of Applied Mathematics , Institute of Technology, Banaras Hindu University , Varanasi, 221 005, India","institution_ids":["https://openalex.org/I91357014"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029915868"],"corresponding_institution_ids":["https://openalex.org/I91357014"],"apc_list":null,"apc_paid":null,"fwci":0.8989,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.73899204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"88","issue":"2","first_page":"430","last_page":"441"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9900000095367432,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9606000185012817,"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/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.9374212026596069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7936937808990479},{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.7792691588401794},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5846533179283142},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.57904452085495},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.5690674781799316},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.5577342510223389},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5291959047317505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43124499917030334},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06901252269744873}],"concepts":[{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.9374212026596069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936937808990479},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.7792691588401794},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5846533179283142},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.57904452085495},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.5690674781799316},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5577342510223389},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5291959047317505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43124499917030334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06901252269744873},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160903474214","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160903474214","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":26,"referenced_works":["https://openalex.org/W7148150","https://openalex.org/W1967339834","https://openalex.org/W1976196891","https://openalex.org/W1977874650","https://openalex.org/W1981126632","https://openalex.org/W1990072901","https://openalex.org/W1993509122","https://openalex.org/W2002138473","https://openalex.org/W2003162364","https://openalex.org/W2009343239","https://openalex.org/W2028587621","https://openalex.org/W2052199721","https://openalex.org/W2054674045","https://openalex.org/W2062298278","https://openalex.org/W2063082611","https://openalex.org/W2077719701","https://openalex.org/W2080340222","https://openalex.org/W2083580538","https://openalex.org/W2087226000","https://openalex.org/W2106912849","https://openalex.org/W2165917005","https://openalex.org/W2240712267","https://openalex.org/W2314271695","https://openalex.org/W2321788680","https://openalex.org/W4245560692","https://openalex.org/W4254879547"],"related_works":["https://openalex.org/W2088506180","https://openalex.org/W2362256999","https://openalex.org/W2188605998","https://openalex.org/W2087729225","https://openalex.org/W2470744056","https://openalex.org/W1964997874","https://openalex.org/W1545358442","https://openalex.org/W4239956528","https://openalex.org/W2040041204","https://openalex.org/W2515699486"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,8,27,42,58],"approximate":[4,64],"analytical":[5],"solutions":[6,66],"of":[7,11,29,49,57],"mathematical":[9,31],"model":[10],"vibration":[12],"equation":[13],"with":[14,26],"fractional-order":[15],"time":[16],"derivative":[17],"\u03b2":[18],"(1<\u03b2\u22642)":[19],"for":[20,62,67],"very":[21],"large":[22],"membranes":[23],"are":[24,60,72],"obtained":[25],"help":[28],"powerful":[30],"tools":[32],"like":[33],"homotopy":[34,38],"perturbation":[35],"method":[36],"and":[37,51,55,76],"analysis":[39],"method.":[40],"Both":[41],"methods":[43],"perform":[44],"extremely":[45],"well":[46],"in":[47],"terms":[48],"efficiency":[50],"simplicity.":[52],"The":[53],"validity":[54],"applicability":[56],"techniques":[59],"shown":[61],"obtaining":[63],"numerical":[65],"different":[68],"particular":[69],"cases":[70],"which":[71],"presented":[73],"through":[74],"figures":[75],"tables.":[77]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}