{"id":"https://openalex.org/W4388676611","doi":"https://doi.org/10.1109/access.2023.3332665","title":"Solving Nonlinear Multi-Order Fractional Differential Equations Using Bernstein Polynomials","display_name":"Solving Nonlinear Multi-Order Fractional Differential Equations Using Bernstein Polynomials","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4388676611","doi":"https://doi.org/10.1109/access.2023.3332665"},"language":"en","primary_location":{"id":"doi:10.1109/access.2023.3332665","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3332665","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10318147.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10318147.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093262835","display_name":"Shahad Adil Taher Algazaa","orcid":"https://orcid.org/0000-0002-5459-7311"},"institutions":[{"id":"https://openalex.org/I181744264","display_name":"Kharazmi University","ror":"https://ror.org/05hsgex59","country_code":"IR","type":"education","lineage":["https://openalex.org/I181744264"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Shahad Adil Taher Algazaa","raw_affiliation_strings":["Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran","Faculty of Mathematical Sciences and Computer, Kharazmi University, No 50, Talegani Ave.,Tehran,1561836314,Iran"],"raw_orcid":"https://orcid.org/0000-0002-5459-7311","affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran","institution_ids":["https://openalex.org/I181744264"]},{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Kharazmi University, No 50, Talegani Ave.,Tehran,1561836314,Iran","institution_ids":["https://openalex.org/I181744264"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038030102","display_name":"Jamshid Saeidian","orcid":"https://orcid.org/0000-0003-3991-1701"},"institutions":[{"id":"https://openalex.org/I181744264","display_name":"Kharazmi University","ror":"https://ror.org/05hsgex59","country_code":"IR","type":"education","lineage":["https://openalex.org/I181744264"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Jamshid Saeidian","raw_affiliation_strings":["Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran","Faculty of Mathematical Sciences and Computer, Kharazmi University, No 50, Talegani Ave.,Tehran,1561836314,Iran"],"raw_orcid":"https://orcid.org/0000-0003-3991-1701","affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran","institution_ids":["https://openalex.org/I181744264"]},{"raw_affiliation_string":"Faculty of Mathematical Sciences and Computer, Kharazmi University, No 50, Talegani Ave.,Tehran,1561836314,Iran","institution_ids":["https://openalex.org/I181744264"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.6302,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6546384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":null,"first_page":"128032","last_page":"128043"},"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":0.9950000047683716,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5653664469718933},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.5558211803436279},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5344886779785156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5304288864135742},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5088863372802734},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.459205687046051},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4588059186935425},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.44210106134414673},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.4297109842300415},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4100988209247589},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3112581670284271},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.20056363940238953},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.14889106154441833},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.10588505864143372}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5653664469718933},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.5558211803436279},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5344886779785156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5304288864135742},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5088863372802734},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.459205687046051},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4588059186935425},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.44210106134414673},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.4297109842300415},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4100988209247589},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3112581670284271},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.20056363940238953},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.14889106154441833},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.10588505864143372},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2023.3332665","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3332665","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10318147.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:edbc8889c26e410995bd536ee8415dc9","is_oa":true,"landing_page_url":"https://doaj.org/article/edbc8889c26e410995bd536ee8415dc9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 11, Pp 128032-128043 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2023.3332665","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3332665","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10318147.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388676611.pdf","grobid_xml":"https://content.openalex.org/works/W4388676611.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W766931091","https://openalex.org/W1553338987","https://openalex.org/W1584611818","https://openalex.org/W1880890436","https://openalex.org/W2002138473","https://openalex.org/W2007553558","https://openalex.org/W2040756577","https://openalex.org/W2051267624","https://openalex.org/W2065898229","https://openalex.org/W2080102983","https://openalex.org/W2088826361","https://openalex.org/W2090187181","https://openalex.org/W2259227674","https://openalex.org/W2326229342","https://openalex.org/W2364992128","https://openalex.org/W2469000661","https://openalex.org/W2568452074","https://openalex.org/W2777150187","https://openalex.org/W2792027044","https://openalex.org/W2795839441","https://openalex.org/W2966272644","https://openalex.org/W2979317226","https://openalex.org/W3012179709","https://openalex.org/W3183810406","https://openalex.org/W3210758412","https://openalex.org/W4220951051","https://openalex.org/W4221117355","https://openalex.org/W4253937035","https://openalex.org/W4285265544","https://openalex.org/W4288050674","https://openalex.org/W4303970992","https://openalex.org/W4312389114","https://openalex.org/W4316096748","https://openalex.org/W6768270833"],"related_works":["https://openalex.org/W2489863694","https://openalex.org/W2353026275","https://openalex.org/W2099676275","https://openalex.org/W4297612202","https://openalex.org/W2949498383","https://openalex.org/W2015514644","https://openalex.org/W2493096353","https://openalex.org/W1652500118","https://openalex.org/W4294834596","https://openalex.org/W1651872008"],"abstract_inverted_index":{"This":[0,95],"paper":[1],"introduces":[2],"two":[3],"novel":[4,150],"methods":[5,128,151,162],"for":[6,97,115],"solving":[7,175],"multi-order":[8],"fractional":[9,22,34,65,176],"differential":[10,35,177],"equations":[11,36],"using":[12,72],"Bernstein":[13,28,51,68],"polynomials.":[14],"The":[15,40,63],"first":[16],"method,":[17,75],"referred":[18],"to":[19,32],"as":[20],"the":[21,44,47,98,101,110,135,143,157,160],"operational":[23],"matrix":[24,88],"of":[25,27,46,67,100,123,148,159,170],"differentiation":[26],"polynomials,":[29,52],"is":[30,70],"employed":[31],"solve":[33],"with":[37,50,89,117,126],"high":[38],"precision.":[39],"second":[41],"method":[42,49,111],"merges":[43],"development":[45],"collocation":[48],"ensuring":[53],"an":[54],"even":[55],"higher":[56],"accuracy":[57,147,171],"than":[58],"previously":[59],"utilized":[60],"numerical":[61,124],"techniques.":[62],"Caputo":[64],"derivative":[66],"polynomials":[69],"calculated":[71],"a":[73,87,90,121,130,141],"specialized":[74],"that":[76],"combines":[77],"Gauss-Jacobi":[78],"quadrature":[79],"rules":[80],"and":[81,109,129,138,146,172],"three-term":[82],"recurrence":[83],"formulas,":[84],"resulting":[85],"in":[86,168,174],"notably":[91],"small":[92],"condition":[93],"number.":[94],"allows":[96],"solution":[99],"algebraic":[102],"system":[103],"through":[104],"standard":[105],"linear":[106],"algebra":[107],"techniques,":[108],"provides":[112],"substantial":[113],"accuracy,particuarly":[114],"problems":[116],"smooth":[118],"solutions.":[119],"Through":[120],"comparison":[122],"examples":[125],"existing":[127],"physical":[131],"test":[132],"example":[133],"predicting":[134],"spheres":[136],"path":[137],"behavior":[139],"within":[140],"fluid":[142],"practical":[144],"applicability":[145],"our":[149],"were":[152],"demonstrated.":[153],"Utilizing":[154],"MATLAB":[155],"2021,":[156],"efficacy":[158],"presented":[161],"was":[163],"showcased,":[164],"revealing":[165],"superior":[166],"performance":[167],"terms":[169],"reliability":[173],"equations.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}