{"id":"https://openalex.org/W4375950342","doi":"https://doi.org/10.1080/00207160.2023.2212089","title":"A new method of solving the best approximate solution for a nonlinear fractional equation","display_name":"A new method of solving the best approximate solution for a nonlinear fractional equation","publication_year":2023,"publication_date":"2023-05-09","ids":{"openalex":"https://openalex.org/W4375950342","doi":"https://doi.org/10.1080/00207160.2023.2212089"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2023.2212089","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2212089","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/A5101476596","display_name":"Hong Du","orcid":"https://orcid.org/0000-0002-4246-6939"},"institutions":[{"id":"https://openalex.org/I79223203","display_name":"Guangdong Ocean University","ror":"https://ror.org/0462wa640","country_code":"CN","type":"education","lineage":["https://openalex.org/I79223203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Du","raw_affiliation_strings":["College of Mathematics and Computer Science, GuangDong Ocean University, ZhanJiang, Guangdong, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, GuangDong Ocean University, ZhanJiang, Guangdong, People's Republic of China","institution_ids":["https://openalex.org/I79223203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102755652","display_name":"Xinyue Yang","orcid":"https://orcid.org/0009-0002-1968-2091"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyue Yang","raw_affiliation_strings":["College of Earth and Environmental Sciences, Lanzhou University, Lanzhou, Gansu, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Earth and Environmental Sciences, Lanzhou University, Lanzhou, Gansu, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101839453","display_name":"Zhong Chen","orcid":"https://orcid.org/0000-0001-8013-9798"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhong Chen","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101839453"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":0.4486,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56023914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"100","issue":"8","first_page":"1702","last_page":"1718"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987999796867371,"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":0.9987000226974487,"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":0.8250349164009094},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.8008366823196411},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.6220473051071167},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.616646409034729},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5745728611946106},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5365126132965088},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4853631258010864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47519075870513916},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.41676560044288635},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1683039665222168}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8250349164009094},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8008366823196411},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.6220473051071167},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.616646409034729},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5745728611946106},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5365126132965088},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4853631258010864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47519075870513916},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.41676560044288635},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1683039665222168},{"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":1,"locations":[{"id":"doi:10.1080/00207160.2023.2212089","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2212089","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":[{"id":"https://metadata.un.org/sdg/14","display_name":"Life below water","score":0.8600000143051147}],"awards":[{"id":"https://openalex.org/G6307358351","display_name":null,"funder_award_id":"2022A1515010022","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G7598364224","display_name":null,"funder_award_id":"R20050","funder_id":"https://openalex.org/F4320329021","funder_display_name":"Guangdong Ocean University"}],"funders":[{"id":"https://openalex.org/F4320329021","display_name":"Guangdong Ocean University","ror":"https://ror.org/0462wa640"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1527525543","https://openalex.org/W1976734729","https://openalex.org/W2017288915","https://openalex.org/W2034221093","https://openalex.org/W2038152558","https://openalex.org/W2041428283","https://openalex.org/W2048805000","https://openalex.org/W2057303584","https://openalex.org/W2058524173","https://openalex.org/W2063052480","https://openalex.org/W2067040719","https://openalex.org/W2067194130","https://openalex.org/W2110504259","https://openalex.org/W2147169375","https://openalex.org/W2516962718","https://openalex.org/W2587910337","https://openalex.org/W2601529646","https://openalex.org/W2610386373","https://openalex.org/W2755121322","https://openalex.org/W2794500091","https://openalex.org/W2900678304","https://openalex.org/W2910867019","https://openalex.org/W2985489239","https://openalex.org/W3023645647","https://openalex.org/W3139923052","https://openalex.org/W4247375400","https://openalex.org/W6600062641","https://openalex.org/W6966789538"],"related_works":["https://openalex.org/W1607269076","https://openalex.org/W2021432593","https://openalex.org/W2323274059","https://openalex.org/W4296546724","https://openalex.org/W2118718279","https://openalex.org/W2348706538","https://openalex.org/W1522620469","https://openalex.org/W2288349649","https://openalex.org/W3200178185","https://openalex.org/W2034418652"],"abstract_inverted_index":{"AbstractA":[0],"new":[1],"method":[2,85],"of":[3,73,78,106],"solving":[4],"the":[5,25,63,71,76,84,111],"best":[6,64,94],"approximate":[7,65,95],"solution":[8,66],"for":[9],"nonlinear":[10,28,39],"fractional":[11,36,60,90],"equations":[12],"with":[13],"smooth":[14],"and":[15,42,58,120,128],"nonsmooth":[16],"solutions":[17],"in":[18,24,50,75],"reproducing":[19,51],"kernel":[20,52,92],"space":[21,53],"is":[22,67],"proposed":[23],"paper.":[26],"The":[27],"equation":[29,41],"outlines":[30],"some":[31],"important":[32],"equations,":[33],"such":[34],"as":[35],"diffusion-wave":[37],"equation,":[38],"Klein\u2013Gordon":[40],"time-fractional":[43],"sine-Gordon":[44],"equation.":[45],"By":[46],"constructing":[47],"orthonormal":[48,56,61],"bases":[49],"using":[54],"Legendre":[55],"polynomials":[57],"Jacobi":[59],"polynomials,":[62],"obtained":[68],"by":[69,110,117],"searching":[70],"minimum":[72],"residue":[74],"sense":[77],"\u2016\u22c5\u2016C.":[79],"Numerical":[80],"experiments":[81],"verify":[82],"that":[83],"has":[86],"higher":[87],"accuracy.Keywords:":[88],"Nonlinear":[89],"equationreproducing":[91],"spacethe":[93],"solutionnonsmooth":[96],"solutionYYYY":[97],"AMS":[98],"SUBJECT":[99],"CLASSIFICATIONS:":[100],"65M1265N12":[101],"Disclosure":[102],"statementNo":[103],"potential":[104],"conflict":[105],"interest":[107],"was":[108,115],"reported":[109],"authors.Additional":[112],"informationFundingThis":[113],"work":[114],"supported":[116],"Guangdong":[118],"Basic":[119,122],"Applied":[121],"Research":[123],"Foundation":[124],"[grant":[125,132],"no.":[126,133],"2022A1515010022]":[127],"GuangDong":[129],"Ocean":[130],"University":[131],"R20050].":[134]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}