{"id":"https://openalex.org/W4416101616","doi":"https://doi.org/10.3390/axioms14110830","title":"An Efficient Iteration Method for Fixed-Point Approximation and Its Application to Fractional Volterra\u2013Fredholm Integro\u2013Differential Equations","display_name":"An Efficient Iteration Method for Fixed-Point Approximation and Its Application to Fractional Volterra\u2013Fredholm Integro\u2013Differential Equations","publication_year":2025,"publication_date":"2025-11-11","ids":{"openalex":"https://openalex.org/W4416101616","doi":"https://doi.org/10.3390/axioms14110830"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14110830","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110830","pdf_url":"https://www.mdpi.com/2075-1680/14/11/830/pdf?version=1762840024","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/2075-1680/14/11/830/pdf?version=1762840024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004073072","display_name":"Ekta Sharma","orcid":"https://orcid.org/0000-0003-3501-8457"},"institutions":[{"id":"https://openalex.org/I265627732","display_name":"National Institute of Technology Manipur","ror":"https://ror.org/00aazk693","country_code":"IN","type":"education","lineage":["https://openalex.org/I265627732"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ekta Sharma","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"],"raw_orcid":"https://orcid.org/0000-0003-3501-8457","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India","institution_ids":["https://openalex.org/I265627732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045676852","display_name":"Shubham Kumar Mittal","orcid":"https://orcid.org/0009-0009-4555-2160"},"institutions":[{"id":"https://openalex.org/I265627732","display_name":"National Institute of Technology Manipur","ror":"https://ror.org/00aazk693","country_code":"IN","type":"education","lineage":["https://openalex.org/I265627732"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shubham Kumar Mittal","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"],"raw_orcid":"https://orcid.org/0009-0009-4555-2160","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India","institution_ids":["https://openalex.org/I265627732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079721299","display_name":"Sunil Panday","orcid":"https://orcid.org/0000-0002-6860-5220"},"institutions":[{"id":"https://openalex.org/I265627732","display_name":"National Institute of Technology Manipur","ror":"https://ror.org/00aazk693","country_code":"IN","type":"education","lineage":["https://openalex.org/I265627732"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sunil Panday","raw_affiliation_strings":["Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"],"raw_orcid":"https://orcid.org/0000-0002-6860-5220","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India","institution_ids":["https://openalex.org/I265627732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006002266","display_name":"Lorentz J\u00e4ntschi","orcid":"https://orcid.org/0000-0001-8524-743X"},"institutions":[{"id":"https://openalex.org/I158333966","display_name":"Technical University of Cluj-Napoca","ror":"https://ror.org/03r8nwp71","country_code":"RO","type":"education","lineage":["https://openalex.org/I158333966"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Lorentz J\u00e4ntschi","raw_affiliation_strings":["Department of Physics and Chemistry, Technical University of Cluj-Napoca, B.-dul Muncii nr. 103-105, 400641 Cluj-Napoca, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8524-743X","affiliations":[{"raw_affiliation_string":"Department of Physics and Chemistry, Technical University of Cluj-Napoca, B.-dul Muncii nr. 103-105, 400641 Cluj-Napoca, Romania","institution_ids":["https://openalex.org/I158333966"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004073072","https://openalex.org/A5006002266"],"corresponding_institution_ids":["https://openalex.org/I158333966","https://openalex.org/I265627732"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.8055,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75179594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"11","first_page":"830","last_page":"830"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.30329999327659607,"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":0.30329999327659607,"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":0.20340000092983246,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.1404000073671341,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/convergence","display_name":"Convergence (economics)","score":0.7024000287055969},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5113000273704529},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4909999966621399},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4668999910354614},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4519999921321869},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4505999982357025},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.43869999051094055},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.41909998655319214}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7024000287055969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6759999990463257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6097999811172485},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5113000273704529},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4909999966621399},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3472000062465668},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C157449380","wikidata":"https://www.wikidata.org/wiki/Q1030759","display_name":"Fixed-point iteration","level":3,"score":0.3400000035762787},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C142311740","wikidata":"https://www.wikidata.org/wiki/Q1066177","display_name":"Shaping","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14110830","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110830","pdf_url":"https://www.mdpi.com/2075-1680/14/11/830/pdf?version=1762840024","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:4ae8ea4a23ac474083e0a8d7730a4444","is_oa":true,"landing_page_url":"https://doaj.org/article/4ae8ea4a23ac474083e0a8d7730a4444","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 11, p 830 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14110830","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110830","pdf_url":"https://www.mdpi.com/2075-1680/14/11/830/pdf?version=1762840024","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416101616.pdf","grobid_xml":"https://content.openalex.org/works/W4416101616.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1458771408","https://openalex.org/W1996239470","https://openalex.org/W2023358569","https://openalex.org/W2026585769","https://openalex.org/W2045471945","https://openalex.org/W2069435104","https://openalex.org/W2079711316","https://openalex.org/W2088536270","https://openalex.org/W2097593805","https://openalex.org/W2810336376","https://openalex.org/W2890428587","https://openalex.org/W2892204294","https://openalex.org/W2950711104","https://openalex.org/W3085530664","https://openalex.org/W4388017629","https://openalex.org/W4399061973","https://openalex.org/W4399491158","https://openalex.org/W4399783921","https://openalex.org/W4403596891","https://openalex.org/W4407249012","https://openalex.org/W4411681247"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"an":[3],"efficient":[4],"iteration":[5,25],"method":[6,14],"for":[7,64],"fixed-point":[8],"approximation":[9],"in":[10,67],"Banach":[11],"spaces.":[12],"The":[13],"accelerates":[15],"convergence":[16,31],"by":[17],"incorporating":[18],"a":[19],"squared":[20],"operator":[21],"term":[22],"within":[23],"the":[24,55,59],"process.":[26],"Analytical":[27],"proofs":[28],"verify":[29],"its":[30],"and":[32,42,62,69],"stability.":[33],"Comparative":[34],"numerical":[35],"tests":[36],"show":[37],"that":[38],"it":[39],"converges":[40],"faster":[41],"more":[43],"reliably":[44],"than":[45],"established":[46],"Picard-type":[47],"methods.":[48],"Its":[49],"application":[50],"to":[51],"fractional":[52,70],"models":[53],"involving":[54],"Gamma":[56],"function":[57],"highlights":[58],"method\u2019s":[60],"efficiency":[61],"potential":[63],"broader":[65],"use":[66],"nonlinear":[68],"systems.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-11-11T00:00:00"}