{"id":"https://openalex.org/W4385579361","doi":"https://doi.org/10.1007/s11075-023-01630-w","title":"A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations","display_name":"A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations","publication_year":2023,"publication_date":"2023-08-04","ids":{"openalex":"https://openalex.org/W4385579361","doi":"https://doi.org/10.1007/s11075-023-01630-w"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01630-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01630-w","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100365572","display_name":"Yifei Wang","orcid":"https://orcid.org/0000-0002-0364-0893"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifei Wang","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073127393","display_name":"Jin Huang","orcid":"https://orcid.org/0000-0002-2191-4739"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jin Huang","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100444599","display_name":"Hu Li","orcid":"https://orcid.org/0000-0001-8624-8792"},"institutions":[{"id":"https://openalex.org/I4210147228","display_name":"Chengdu Normal University","ror":"https://ror.org/04enz2k98","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147228"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu Li","raw_affiliation_strings":["School of Mathematics, Chengdu Normal University, Chengdu, 611130, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Chengdu Normal University, Chengdu, 611130, China","institution_ids":["https://openalex.org/I4210147228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073127393"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.3567,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51157913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"95","issue":"4","first_page":"1855","last_page":"1877"},"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":0.9983000159263611,"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":0.9923999905586243,"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":0.8810256719589233},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.6085474491119385},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5966048240661621},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5695679187774658},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5541547536849976},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5201842784881592},{"id":"https://openalex.org/keywords/gronwalls-inequality","display_name":"Gronwall's inequality","score":0.5170072317123413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5108006000518799},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4864654242992401},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4744352400302887},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45754051208496094},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4535865783691406},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.43679705262184143},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4305006265640259},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4297628402709961},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.37033993005752563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8810256719589233},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.6085474491119385},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5966048240661621},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5695679187774658},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5541547536849976},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5201842784881592},{"id":"https://openalex.org/C37608338","wikidata":"https://www.wikidata.org/wiki/Q510733","display_name":"Gronwall's inequality","level":3,"score":0.5170072317123413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5108006000518799},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4864654242992401},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4744352400302887},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45754051208496094},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4535865783691406},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.43679705262184143},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4305006265640259},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4297628402709961},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.37033993005752563},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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:10.1007/s11075-023-01630-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01630-w","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2305840303","display_name":null,"funder_award_id":"2022NSFSC1844","funder_id":"https://openalex.org/F4320329861","funder_display_name":"Natural Science Foundation of Sichuan Province"},{"id":"https://openalex.org/G906727408","display_name":null,"funder_award_id":"12101089","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"},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W199952430","https://openalex.org/W625596342","https://openalex.org/W1567668233","https://openalex.org/W1570089119","https://openalex.org/W1968735445","https://openalex.org/W1969399740","https://openalex.org/W1975443030","https://openalex.org/W1980867546","https://openalex.org/W2021492437","https://openalex.org/W2021735811","https://openalex.org/W2036013247","https://openalex.org/W2063133641","https://openalex.org/W2066229481","https://openalex.org/W2082998953","https://openalex.org/W2105723279","https://openalex.org/W2107162131","https://openalex.org/W2137696066","https://openalex.org/W2143113918","https://openalex.org/W2149846618","https://openalex.org/W2155720716","https://openalex.org/W2168857596","https://openalex.org/W2218598941","https://openalex.org/W2330381107","https://openalex.org/W2408637982","https://openalex.org/W2595252265","https://openalex.org/W2707805209","https://openalex.org/W2742489936","https://openalex.org/W2755846920","https://openalex.org/W2770671996","https://openalex.org/W2924730450","https://openalex.org/W2928839578","https://openalex.org/W2938011410","https://openalex.org/W2942011276","https://openalex.org/W2963589517","https://openalex.org/W2980535862","https://openalex.org/W3007046170","https://openalex.org/W3034658329","https://openalex.org/W3083942293","https://openalex.org/W3096557529","https://openalex.org/W3137224107","https://openalex.org/W3192083077","https://openalex.org/W4206565825","https://openalex.org/W4213150297","https://openalex.org/W4252219081","https://openalex.org/W4252371218","https://openalex.org/W4253937035","https://openalex.org/W4295067862","https://openalex.org/W4312107723"],"related_works":["https://openalex.org/W4388522829","https://openalex.org/W2519730419","https://openalex.org/W2254680073","https://openalex.org/W2282343183","https://openalex.org/W2103893721","https://openalex.org/W2006021087","https://openalex.org/W1996416189","https://openalex.org/W2182117216","https://openalex.org/W3174665301","https://openalex.org/W2083073512"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}