{"id":"https://openalex.org/W4402488464","doi":"https://doi.org/10.3390/axioms13090621","title":"Analytical and Numerical Approaches via Quadratic Integral Equations","display_name":"Analytical and Numerical Approaches via Quadratic Integral Equations","publication_year":2024,"publication_date":"2024-09-12","ids":{"openalex":"https://openalex.org/W4402488464","doi":"https://doi.org/10.3390/axioms13090621"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13090621","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090621","pdf_url":"https://www.mdpi.com/2075-1680/13/9/621/pdf?version=1726132078","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/9/621/pdf?version=1726132078","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052075016","display_name":"Jihan Alahmadi","orcid":"https://orcid.org/0000-0003-1457-6927"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Jihan Alahmadi","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1457-6927","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009856714","display_name":"M.A. Abdou","orcid":"https://orcid.org/0000-0003-4114-3553"},"institutions":[{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohamed A. Abdou","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21511, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21511, Egypt","institution_ids":["https://openalex.org/I84524832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035052265","display_name":"M. A. Abdel\u2013Aty","orcid":"https://orcid.org/0000-0001-5865-278X"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Mohamed A. Abdel-Aty","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Science, Benha University, Benha 13518, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-5865-278X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035052265"],"corresponding_institution_ids":["https://openalex.org/I207547235"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3277,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55425379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"9","first_page":"621","last_page":"621"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9984999895095825,"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":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9886000156402588,"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/quadratic-equation","display_name":"Quadratic equation","score":0.6059713959693909},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5509063005447388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5403982996940613},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5244189500808716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33370018005371094},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3285970091819763},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10556992888450623},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0560297966003418}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6059713959693909},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5509063005447388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5403982996940613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5244189500808716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33370018005371094},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3285970091819763},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10556992888450623},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0560297966003418},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13090621","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090621","pdf_url":"https://www.mdpi.com/2075-1680/13/9/621/pdf?version=1726132078","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:599ef12aecc349718d0b47f7c218b816","is_oa":false,"landing_page_url":"https://doaj.org/article/599ef12aecc349718d0b47f7c218b816","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 9, p 621 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13090621","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090621","pdf_url":"https://www.mdpi.com/2075-1680/13/9/621/pdf?version=1726132078","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311227","display_name":"Prince Sattam bin Abdulaziz University","ror":"https://ror.org/04jt46d36"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402488464.pdf","grobid_xml":"https://content.openalex.org/works/W4402488464.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1667970384","https://openalex.org/W1864172083","https://openalex.org/W2036013247","https://openalex.org/W2056481665","https://openalex.org/W2124714823","https://openalex.org/W2212759539","https://openalex.org/W2327629093","https://openalex.org/W2534904951","https://openalex.org/W2547557075","https://openalex.org/W2553506003","https://openalex.org/W2608802507","https://openalex.org/W2746233099","https://openalex.org/W2802642012","https://openalex.org/W3007046170","https://openalex.org/W3024238337","https://openalex.org/W3094204174","https://openalex.org/W3103787787","https://openalex.org/W3137918392","https://openalex.org/W4283376759","https://openalex.org/W4283659700","https://openalex.org/W4288052984","https://openalex.org/W4288085597","https://openalex.org/W4310169454","https://openalex.org/W4312101040","https://openalex.org/W4318973005","https://openalex.org/W4322623826","https://openalex.org/W4361768836","https://openalex.org/W4365394502","https://openalex.org/W4376117128","https://openalex.org/W4387109776","https://openalex.org/W4387264558","https://openalex.org/W4387851008","https://openalex.org/W4398776995","https://openalex.org/W6637081885","https://openalex.org/W6664626294","https://openalex.org/W6678882489","https://openalex.org/W6688633918","https://openalex.org/W6729448436"],"related_works":["https://openalex.org/W2031561209","https://openalex.org/W1973641256","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W1121942432","https://openalex.org/W2418069309","https://openalex.org/W2103176649","https://openalex.org/W2376158287","https://openalex.org/W2040562223","https://openalex.org/W2785906022"],"abstract_inverted_index":{"A":[0],"quadratic":[1,54],"integral":[2,55,65,88],"Equation":[3],"(QIE)":[4],"of":[5,20,40,43,51,64,67,78,87,102,115,131],"the":[6,15,26,41,44,48,68,72,76,85,93,100,103,111,116,132,135],"second":[7,69],"kind":[8,70],"with":[9,122],"continuous":[10],"kernels":[11],"is":[12,28,90,105],"solved":[13,91],"in":[14,30],"space":[16],"C([0,T]\u00d7[0,T]).":[17],"The":[18,53],"existence":[19],"at":[21],"least":[22],"one":[23],"solution":[24],"to":[25,60,128],"QIE":[27],"discussed":[29],"this":[31],"article.":[32],"Our":[33],"evidence":[34],"depends":[35],"on":[36],"a":[37,62],"suitable":[38],"combination":[39],"measures":[42],"noncompactness":[45],"approach":[46],"and":[47,83,113],"fixed-point":[49],"principle":[50],"Darbo.":[52],"equation":[56],"can":[57],"be":[58],"used":[59,127],"derive":[61],"system":[63,86],"equations":[66,89],"using":[71,92,108],"quadrature":[73],"method.":[74,95],"With":[75],"aid":[77],"two":[79],"different":[80],"polynomials,":[81],"Laguerre":[82],"Hermite,":[84],"collocation":[94],"In":[96],"each":[97],"numerical":[98],"approach,":[99],"estimation":[101],"error":[104],"discussed.":[106],"Finally,":[107],"some":[109],"examples,":[110],"accuracy":[112],"scalability":[114],"proposed":[117],"method":[118],"are":[119],"demonstrated":[120],"along":[121],"comparisons.":[123],"Mathematica":[124],"11":[125],"was":[126],"obtain":[129],"all":[130],"results":[133],"from":[134],"techniques":[136],"that":[137],"were":[138],"shown.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}