{"id":"https://openalex.org/W4406725306","doi":"https://doi.org/10.1007/s11075-024-02005-5","title":"A numerical approach for solving fractional order pantograph mixed Volterra-Fredholm delay-integro-differential equations","display_name":"A numerical approach for solving fractional order pantograph mixed Volterra-Fredholm delay-integro-differential equations","publication_year":2025,"publication_date":"2025-01-21","ids":{"openalex":"https://openalex.org/W4406725306","doi":"https://doi.org/10.1007/s11075-024-02005-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-024-02005-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-02005-5","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/A5046275509","display_name":"Yifei Wang","orcid":"https://orcid.org/0000-0002-0006-6152"},"institutions":[{"id":"https://openalex.org/I102345215","display_name":"Xihua University","ror":"https://ror.org/04gwtvf26","country_code":"CN","type":"education","lineage":["https://openalex.org/I102345215"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yifei Wang","raw_affiliation_strings":["School of Science, Xihua University, Chengdu, 610039, China","School of Science, Xihua University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xihua University, Chengdu, 610039, China","institution_ids":["https://openalex.org/I102345215"]},{"raw_affiliation_string":"School of Science, Xihua University, Chengdu, China","institution_ids":["https://openalex.org/I102345215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100425521","display_name":"Li Zhang","orcid":"https://orcid.org/0000-0002-1999-6819"},"institutions":[{"id":"https://openalex.org/I102345215","display_name":"Xihua University","ror":"https://ror.org/04gwtvf26","country_code":"CN","type":"education","lineage":["https://openalex.org/I102345215"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Zhang","raw_affiliation_strings":["School of Science, Xihua University, Chengdu, 610039, China","School of Science, Xihua University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xihua University, Chengdu, 610039, China","institution_ids":["https://openalex.org/I102345215"]},{"raw_affiliation_string":"School of Science, Xihua University, Chengdu, China","institution_ids":["https://openalex.org/I102345215"]}]},{"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":true,"raw_author_name":"Hu Li","raw_affiliation_strings":["School of Mathematics, Chengdu Normal University, Chengdu, 611130, China","School of Mathematics, Chengdu Normal University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Chengdu Normal University, Chengdu, 611130, China","institution_ids":["https://openalex.org/I4210147228"]},{"raw_affiliation_string":"School of Mathematics, Chengdu Normal University, Chengdu, China","institution_ids":["https://openalex.org/I4210147228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046275509","https://openalex.org/A5100425521","https://openalex.org/A5100444599"],"corresponding_institution_ids":["https://openalex.org/I102345215","https://openalex.org/I4210147228"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.7827,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.6190823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"101","issue":"1","first_page":"273","last_page":"299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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":0.9994000196456909,"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/T12197","display_name":"Brake Systems and Friction Analysis","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.986299991607666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7954012155532837},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7068121433258057},{"id":"https://openalex.org/keywords/volterra-equations","display_name":"Volterra equations","score":0.6132824420928955},{"id":"https://openalex.org/keywords/pantograph","display_name":"Pantograph","score":0.5737122297286987},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5571202039718628},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5065876245498657},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47634437680244446},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4694259762763977},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46429142355918884},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4334392547607422},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3463212847709656},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22619372606277466},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07712215185165405},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06642952561378479}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7954012155532837},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7068121433258057},{"id":"https://openalex.org/C2983756050","wikidata":"https://www.wikidata.org/wiki/Q150052","display_name":"Volterra equations","level":3,"score":0.6132824420928955},{"id":"https://openalex.org/C20756127","wikidata":"https://www.wikidata.org/wiki/Q722757","display_name":"Pantograph","level":2,"score":0.5737122297286987},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5571202039718628},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5065876245498657},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47634437680244446},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4694259762763977},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46429142355918884},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4334392547607422},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3463212847709656},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22619372606277466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07712215185165405},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06642952561378479},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-024-02005-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-02005-5","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1605182429","https://openalex.org/W1972995042","https://openalex.org/W1982807058","https://openalex.org/W2000017501","https://openalex.org/W2009047796","https://openalex.org/W2021492437","https://openalex.org/W2024842502","https://openalex.org/W2036013247","https://openalex.org/W2041875300","https://openalex.org/W2043665547","https://openalex.org/W2068738719","https://openalex.org/W2072349082","https://openalex.org/W2083796394","https://openalex.org/W2116807840","https://openalex.org/W2405981400","https://openalex.org/W2591985654","https://openalex.org/W2641679988","https://openalex.org/W2742489936","https://openalex.org/W2808933267","https://openalex.org/W2946910752","https://openalex.org/W2947507964","https://openalex.org/W2947647030","https://openalex.org/W2994446770","https://openalex.org/W3005237029","https://openalex.org/W3007342316","https://openalex.org/W3011010596","https://openalex.org/W3011238522","https://openalex.org/W3019185786","https://openalex.org/W3037285524","https://openalex.org/W3086049432","https://openalex.org/W3117671761","https://openalex.org/W3137285274","https://openalex.org/W3186422528","https://openalex.org/W3186546279","https://openalex.org/W3202173002","https://openalex.org/W3204790508","https://openalex.org/W4223977018","https://openalex.org/W4239114676","https://openalex.org/W4240465921","https://openalex.org/W4249137419","https://openalex.org/W4296213122","https://openalex.org/W4310275918","https://openalex.org/W4400300731","https://openalex.org/W4401109489"],"related_works":["https://openalex.org/W2082102072","https://openalex.org/W2517687681","https://openalex.org/W2118560105","https://openalex.org/W2358959122","https://openalex.org/W4401089097","https://openalex.org/W4249149186","https://openalex.org/W4225984655","https://openalex.org/W2031624200","https://openalex.org/W1541040149","https://openalex.org/W1539637428"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
