{"id":"https://openalex.org/W2604960675","doi":"https://doi.org/10.3233/fi-2017-1503","title":"A New Optimization Method Based on Generalized Polynomials for Fractional Differential Equations","display_name":"A New Optimization Method Based on Generalized Polynomials for Fractional Differential Equations","publication_year":2017,"publication_date":"2017-03-11","ids":{"openalex":"https://openalex.org/W2604960675","doi":"https://doi.org/10.3233/fi-2017-1503","mag":"2604960675"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2017-1503","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1503","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5040688350","display_name":"Hossein Hassani","orcid":"https://orcid.org/0000-0001-6916-1492"},"institutions":[{"id":"https://openalex.org/I127908078","display_name":"Shahrekord University","ror":"https://ror.org/051rngw70","country_code":"IR","type":"education","lineage":["https://openalex.org/I127908078"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hossein Hassani","raw_affiliation_strings":["Department of Mathematics, Shahrekord University, Shahrekord, Iran. hosseinhassani40@yahoo.com, msh-dahaghin@sci.sku.ac.ir"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahrekord University, Shahrekord, Iran. hosseinhassani40@yahoo.com, msh-dahaghin@sci.sku.ac.ir","institution_ids":["https://openalex.org/I127908078"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012718873","display_name":"Mohammad Shafie Dahaghin","orcid":null},"institutions":[{"id":"https://openalex.org/I127908078","display_name":"Shahrekord University","ror":"https://ror.org/051rngw70","country_code":"IR","type":"education","lineage":["https://openalex.org/I127908078"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Shafie Dahaghin","raw_affiliation_strings":["Department of Mathematics, Shahrekord University, Shahrekord, Iran. hosseinhassani40@yahoo.com, msh-dahaghin@sci.sku.ac.ir"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahrekord University, Shahrekord, Iran. hosseinhassani40@yahoo.com, msh-dahaghin@sci.sku.ac.ir","institution_ids":["https://openalex.org/I127908078"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Mohammad Hossein Heydari","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161235","display_name":"Fasa University of Medical Sciences","ror":"https://ror.org/05bh0zx16","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210161235"]},{"id":"https://openalex.org/I4400600978","display_name":"Fasa University","ror":"https://ror.org/03a77cf20","country_code":null,"type":"education","lineage":["https://openalex.org/I4400600978"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mohammad Hossein Heydari","raw_affiliation_strings":["Department of Mathematics, Fasa University, Fasa, Iran. heydari@fasau.ac.ir"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Fasa University, Fasa, Iran. heydari@fasau.ac.ir","institution_ids":["https://openalex.org/I4210161235","https://openalex.org/I4400600978"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042373628","display_name":"Ali Bayati Eshkaftaki","orcid":"https://orcid.org/0000-0003-3979-0823"},"institutions":[{"id":"https://openalex.org/I127908078","display_name":"Shahrekord University","ror":"https://ror.org/051rngw70","country_code":"IR","type":"education","lineage":["https://openalex.org/I127908078"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Bayati Eshkaftaki","raw_affiliation_strings":["Department of Mathematics, Shahrekord University, Shahrekord, Iran. bayati.ali@sci.sku.ac.ir"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shahrekord University, Shahrekord, Iran. bayati.ali@sci.sku.ac.ir","institution_ids":["https://openalex.org/I127908078"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210161235","https://openalex.org/I4400600978"],"apc_list":null,"apc_paid":null,"fwci":0.3214,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56750131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"151","issue":"1-4","first_page":"443","last_page":"457"},"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":0.9976999759674072,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9812999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8006395101547241},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6034711599349976},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5532525777816772},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5371732115745544},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5046268701553345},{"id":"https://openalex.org/keywords/method-of-mean-weighted-residuals","display_name":"Method of mean weighted residuals","score":0.4675307273864746},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.42767006158828735},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4248017966747284},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4040696620941162},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27613869309425354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15914031863212585},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.08053275942802429}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8006395101547241},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6034711599349976},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5532525777816772},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5371732115745544},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5046268701553345},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.4675307273864746},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42767006158828735},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4248017966747284},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4040696620941162},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27613869309425354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15914031863212585},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.08053275942802429},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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:10.3233/fi-2017-1503","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1503","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W75450506","https://openalex.org/W594457519","https://openalex.org/W770652455","https://openalex.org/W846923873","https://openalex.org/W1127902823","https://openalex.org/W1509146820","https://openalex.org/W1550268283","https://openalex.org/W1965027360","https://openalex.org/W1969446688","https://openalex.org/W1970741096","https://openalex.org/W1975383112","https://openalex.org/W1975670568","https://openalex.org/W1976404793","https://openalex.org/W1978848705","https://openalex.org/W1992122601","https://openalex.org/W1993445800","https://openalex.org/W1994916853","https://openalex.org/W2001514844","https://openalex.org/W2004845306","https://openalex.org/W2005114389","https://openalex.org/W2005455954","https://openalex.org/W2010016067","https://openalex.org/W2022072871","https://openalex.org/W2022815635","https://openalex.org/W2029199104","https://openalex.org/W2033744839","https://openalex.org/W2041437724","https://openalex.org/W2042923669","https://openalex.org/W2043532630","https://openalex.org/W2043742654","https://openalex.org/W2058330335","https://openalex.org/W2060462514","https://openalex.org/W2062163287","https://openalex.org/W2063133641","https://openalex.org/W2063271632","https://openalex.org/W2063741379","https://openalex.org/W2065094385","https://openalex.org/W2071593170","https://openalex.org/W2103233901","https://openalex.org/W2175588415","https://openalex.org/W2228681942","https://openalex.org/W2282745915","https://openalex.org/W2466433738","https://openalex.org/W2787959293","https://openalex.org/W2944855064"],"related_works":["https://openalex.org/W4392389852","https://openalex.org/W4408806508","https://openalex.org/W2099433359","https://openalex.org/W2418863753","https://openalex.org/W2745121476","https://openalex.org/W2995651557","https://openalex.org/W4367701160","https://openalex.org/W2106833662","https://openalex.org/W2963101856","https://openalex.org/W4253473935"],"abstract_inverted_index":{"In":[0,29],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5,11,95,106],"new":[6,12],"optimization":[7,81],"method":[8,139],"based":[9],"on":[10],"class":[13],"of":[14,35,44,101,108,123],"functions,":[15],"namely":[16],"generalized":[17],"polynomials":[18],"(GPs)":[19],"for":[20,73],"solving":[21],"linear":[22],"and":[23,52,68,83,90,116,121,143],"nonlinear":[24,109],"fractional":[25],"differential":[26],"equations":[27,111],"(FDEs).":[28],"the":[30,33,36,45,62,75,86,98,124,137],"proposed":[31,138],"method,":[32],"solution":[34],"problem":[37,76],"under":[38,77],"study":[39],"is":[40,140],"expanded":[41],"in":[42],"terms":[43],"GPs":[46],"with":[47,112],"fixed":[48,63],"coefficients,":[49],"free":[50,88,114],"coefficients":[51,89,115],"control":[53,91,117],"parameters.":[54,118],"The":[55,65,119,132],"initial":[56],"conditions":[57,100],"are":[58,71,103,126],"employed":[59,72],"to":[60,79],"compute":[61],"coefficients.":[64],"residual":[66],"function":[67],"its":[69],"\u2016.\u20162":[70],"converting":[74],"consideration":[78],"an":[80],"one":[82],"then":[84],"choosing":[85],"unknown":[87,113],"parameters":[92],"optimally.":[93],"As":[94],"useful":[96],"result,":[97],"necessary":[99],"optimality":[102],"derived":[104],"as":[105],"system":[107],"algebraic":[110],"validity":[120],"accuracy":[122],"approach":[125],"illustrated":[127],"by":[128],"some":[129],"numerical":[130],"examples.":[131],"obtained":[133],"results":[134],"show":[135],"that":[136],"very":[141],"efficient":[142],"accurate.":[144]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}
