{"id":"https://openalex.org/W2998165478","doi":"https://doi.org/10.1007/s11075-019-00858-9","title":"A new stable collocation method for solving a class of nonlinear fractional delay differential equations","display_name":"A new stable collocation method for solving a class of nonlinear fractional delay differential equations","publication_year":2020,"publication_date":"2020-01-04","ids":{"openalex":"https://openalex.org/W2998165478","doi":"https://doi.org/10.1007/s11075-019-00858-9","mag":"2998165478"},"language":"lv","primary_location":{"id":"doi:10.1007/s11075-019-00858-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-019-00858-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-019-00858-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-019-00858-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101666035","display_name":"Lei Shi","orcid":"https://orcid.org/0000-0003-1737-9187"},"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":"Lei Shi","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Weihai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Weihai, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","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":false,"raw_author_name":"Zhong Chen","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Weihai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Weihai, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101413900","display_name":"Xiaohua Ding","orcid":"https://orcid.org/0000-0002-0983-3522"},"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":false,"raw_author_name":"Xiaohua Ding","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Weihai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Weihai, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033691077","display_name":"Qiang Ma","orcid":"https://orcid.org/0000-0001-6839-1827"},"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":false,"raw_author_name":"Qiang Ma","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Weihai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Weihai, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101666035"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3789,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.67203069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"85","issue":"4","first_page":"1123","last_page":"1153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.5915533900260925},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46981316804885864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43029066920280457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35753577947616577},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16174256801605225}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5915533900260925},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46981316804885864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43029066920280457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35753577947616577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16174256801605225},{"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:10.1007/s11075-019-00858-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-019-00858-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-019-00858-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-019-00858-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-019-00858-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-019-00858-9.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1081347284","display_name":null,"funder_award_id":"11501150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2998165478.pdf","grobid_xml":"https://content.openalex.org/works/W2998165478.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W273630147","https://openalex.org/W750857168","https://openalex.org/W1592141884","https://openalex.org/W1970004356","https://openalex.org/W1975670568","https://openalex.org/W1984696323","https://openalex.org/W1989758007","https://openalex.org/W1999141406","https://openalex.org/W2013958055","https://openalex.org/W2029497261","https://openalex.org/W2057303584","https://openalex.org/W2058191269","https://openalex.org/W2063942220","https://openalex.org/W2181255906","https://openalex.org/W2510881444","https://openalex.org/W2569274492","https://openalex.org/W2597664725","https://openalex.org/W2754157234","https://openalex.org/W2771931031","https://openalex.org/W2794500091","https://openalex.org/W2801192398","https://openalex.org/W3106900341","https://openalex.org/W3143329128","https://openalex.org/W4242212920"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"a":[4,20,75,84,97],"stable":[5],"collocation":[6],"method":[7,68],"for":[8,89],"solving":[9,96],"the":[10,40,48,51,60,71,81,103,117,120],"nonlinear":[11,61,72],"fractional":[12],"delay":[13],"differential":[14],"equations":[15,100],"is":[16,87,108],"proposed":[17,121],"by":[18,95],"constructing":[19],"new":[21],"set":[22],"of":[23,27,34,50,53,66,77,99,119],"multiscale":[24],"orthonormal":[25],"bases":[26],"$W^{1}_{2,0}$":[28],"<mml:math":[29,55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msubsup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math>":[30,56],".":[31,57],"Error":[32],"estimations":[33],"approximate":[35],"solutions":[36,94],"are":[37,113],"given":[38,88],"and":[39],"highest":[41],"convergence":[42],"order":[43],"can":[44],"reach":[45],"four":[46],"in":[47],"sense":[49],"norm":[52],"$W_{2,0}^{1}$":[54],"To":[58],"overcome":[59],"condition,":[62],"we":[63],"make":[64],"use":[65],"Newton\u2019s":[67],"to":[69,115],"transform":[70],"equation":[73],"into":[74],"sequence":[76],"linear":[78,82],"equations.":[79],"For":[80],"equations,":[83],"rigorous":[85],"theory":[86],"obtaining":[90],"their":[91],"\u03b5":[92],"-approximate":[93],"system":[98],"or":[101],"searching":[102],"minimum":[104],"value.":[105],"Stability":[106],"analysis":[107],"also":[109],"obtained.":[110],"Some":[111],"examples":[112],"discussed":[114],"illustrate":[116],"efficiency":[118],"method.":[122]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
