{"id":"https://openalex.org/W2953364340","doi":"https://doi.org/10.1007/s10915-019-00987-2","title":"A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels","display_name":"A Fractional Spectral Collocation for Solving Second Kind Nonlinear Volterra Integral Equations with Weakly Singular Kernels","publication_year":2019,"publication_date":"2019-06-12","ids":{"openalex":"https://openalex.org/W2953364340","doi":"https://doi.org/10.1007/s10915-019-00987-2","mag":"2953364340"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-019-00987-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00987-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","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/A5040370931","display_name":"Haotao Cai","orcid":"https://orcid.org/0000-0002-0278-2945"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haotao Cai","raw_affiliation_strings":["School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, Shandong, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, Shandong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I59483232"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040370931"],"corresponding_institution_ids":["https://openalex.org/I59483232"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.9038,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.72765169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"80","issue":"3","first_page":"1529","last_page":"1548"},"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":0.9979000091552734,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.8806694746017456},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6706552505493164},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6135425567626953},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5850214958190918},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.579914391040802},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5371675491333008},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5290504693984985},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5164127945899963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47186583280563354},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.47152623534202576},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4470929801464081},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4134272038936615},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1104501485824585}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8806694746017456},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6706552505493164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6135425567626953},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5850214958190918},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.579914391040802},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5371675491333008},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5290504693984985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5164127945899963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47186583280563354},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.47152623534202576},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4470929801464081},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4134272038936615},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1104501485824585},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-019-00987-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-019-00987-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5163235521","display_name":null,"funder_award_id":"ZR2014JL003","funder_id":"https://openalex.org/F4320313896","funder_display_name":"Department of Education of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320313896","display_name":"Department of Education of Shandong Province","ror":"https://ror.org/01ksk4k18"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W205381016","https://openalex.org/W640428934","https://openalex.org/W1567668233","https://openalex.org/W1970230688","https://openalex.org/W1977298783","https://openalex.org/W1978958071","https://openalex.org/W1979762896","https://openalex.org/W1979950678","https://openalex.org/W1981025556","https://openalex.org/W1984967418","https://openalex.org/W1994678449","https://openalex.org/W2012144921","https://openalex.org/W2014208709","https://openalex.org/W2015622021","https://openalex.org/W2020988386","https://openalex.org/W2024169233","https://openalex.org/W2028224531","https://openalex.org/W2052623210","https://openalex.org/W2055212013","https://openalex.org/W2060819023","https://openalex.org/W2065254635","https://openalex.org/W2071860534","https://openalex.org/W2073689707","https://openalex.org/W2118288723","https://openalex.org/W2145736329","https://openalex.org/W2151276461","https://openalex.org/W2151640244","https://openalex.org/W2192231559","https://openalex.org/W2270749385","https://openalex.org/W2301264260","https://openalex.org/W2316383984","https://openalex.org/W2324921170","https://openalex.org/W2339840080","https://openalex.org/W2342026602","https://openalex.org/W2486941867","https://openalex.org/W2553651416","https://openalex.org/W2602777695","https://openalex.org/W2762055348","https://openalex.org/W2778387726","https://openalex.org/W2889815288","https://openalex.org/W2916289141","https://openalex.org/W4253937035","https://openalex.org/W4300200902"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2889856026","https://openalex.org/W2009058751","https://openalex.org/W1989122168","https://openalex.org/W2131278000","https://openalex.org/W2953063785"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}