{"id":"https://openalex.org/W7165036912","doi":"https://doi.org/10.3846/mma.2026.24019","title":"Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it","display_name":"Solvability of two-dimensional nonlinear singular Volterra integral equations with fractional order in Banach space and approximation of the solution of it","publication_year":2026,"publication_date":"2026-06-17","ids":{"openalex":"https://openalex.org/W7165036912","doi":"https://doi.org/10.3846/mma.2026.24019"},"language":"en","primary_location":{"id":"doi:10.3846/mma.2026.24019","is_oa":true,"landing_page_url":"https://doi.org/10.3846/mma.2026.24019","pdf_url":"https://journals.vilniustech.lt/index.php/MMA/article/download/24019/13420","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.vilniustech.lt/index.php/MMA/article/download/24019/13420","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094056790","display_name":"Samaneh Darvishi Khezri","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086811","display_name":"Islamic Azad University Sari Branch","ror":"https://ror.org/0032wgp28","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210086811"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Samaneh Darvishi Khezri","raw_affiliation_strings":["Department of Mathematics, Sar.C., Islamic Azad University"],"raw_orcid":"https://orcid.org/0009-0002-1179-4734","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sar.C., Islamic Azad University","institution_ids":["https://openalex.org/I4210086811"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138788343","display_name":"Mohsen Rabbani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086811","display_name":"Islamic Azad University Sari Branch","ror":"https://ror.org/0032wgp28","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210086811"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohsen Rabbani","raw_affiliation_strings":["Department of Mathematics, Sar.C., Islamic Azad University"],"raw_orcid":"https://orcid.org/0000-0003-3602-6125","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sar.C., Islamic Azad University","institution_ids":["https://openalex.org/I4210086811"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013070122","display_name":"Reza Arab","orcid":"https://orcid.org/0000-0002-3790-4703"},"institutions":[{"id":"https://openalex.org/I4210086811","display_name":"Islamic Azad University Sari Branch","ror":"https://ror.org/0032wgp28","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210086811"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Reza Arab","raw_affiliation_strings":["Department of Mathematics, Sar.C., Islamic Azad University"],"raw_orcid":"https://orcid.org/0000-0002-3790-4703","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sar.C., Islamic Azad University","institution_ids":["https://openalex.org/I4210086811"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012522025","display_name":"Vahid Dadashi","orcid":"https://orcid.org/0000-0003-3289-0426"},"institutions":[{"id":"https://openalex.org/I4210086811","display_name":"Islamic Azad University Sari Branch","ror":"https://ror.org/0032wgp28","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210086811"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Vahid Dadashi","raw_affiliation_strings":["Department of Mathematics, Sar.C., Islamic Azad University"],"raw_orcid":"https://orcid.org/0000-0003-3289-0426","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sar.C., Islamic Azad University","institution_ids":["https://openalex.org/I4210086811"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210086811"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.79390448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"3","first_page":"407","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.5156000256538391,"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":0.5156000256538391,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.4250999987125397,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.020999999716877937,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/banach-space","display_name":"Banach space","score":0.6955999732017517},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6747000217437744},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5580999851226807},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.519599974155426},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.4894999861717224},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.48170000314712524},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.48089998960494995},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47839999198913574},{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.40720000863075256}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8917999863624573},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6955999732017517},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6747000217437744},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5684000253677368},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5580999851226807},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.519599974155426},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.4894999861717224},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.48170000314712524},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.48089998960494995},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.40720000863075256},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4009000062942505},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3776000142097473},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.3325999975204468},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.258899986743927}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3846/mma.2026.24019","is_oa":true,"landing_page_url":"https://doi.org/10.3846/mma.2026.24019","pdf_url":"https://journals.vilniustech.lt/index.php/MMA/article/download/24019/13420","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8787f57178b94f57b16b760535702c0b","is_oa":false,"landing_page_url":"https://doaj.org/article/8787f57178b94f57b16b760535702c0b","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":"Mathematical Modelling and Analysis, Vol 31, Iss 3 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3846/mma.2026.24019","is_oa":true,"landing_page_url":"https://doi.org/10.3846/mma.2026.24019","pdf_url":"https://journals.vilniustech.lt/index.php/MMA/article/download/24019/13420","source":{"id":"https://openalex.org/S177394553","display_name":"Mathematical Modelling and Analysis","issn_l":"1392-6292","issn":["1392-6292","1648-3510"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7165036912.pdf","grobid_xml":"https://content.openalex.org/works/W7165036912.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1976308021","https://openalex.org/W1981067137","https://openalex.org/W2010372803","https://openalex.org/W2074668063","https://openalex.org/W2092568001","https://openalex.org/W2132795750","https://openalex.org/W2589070614","https://openalex.org/W2600516003","https://openalex.org/W2763535636","https://openalex.org/W2791876403","https://openalex.org/W2886191658","https://openalex.org/W2944997840","https://openalex.org/W2949703622","https://openalex.org/W2955796084","https://openalex.org/W2971402712","https://openalex.org/W3085450669","https://openalex.org/W3125988921","https://openalex.org/W3130649380","https://openalex.org/W3217294025","https://openalex.org/W4224326399","https://openalex.org/W4379987991","https://openalex.org/W4388578938","https://openalex.org/W4389925758","https://openalex.org/W4410114924","https://openalex.org/W4413087966"],"related_works":[],"abstract_inverted_index":{"In":[0,37],"this":[1,39],"article,":[2],"existence":[3],"and":[4,34],"uniqueness":[5],"of":[6,29,32,41,46,57,69,74,85,107],"the":[7,27,30,55,58,67,75,83,105,108,111],"solution":[8,56,93],"for":[9,94],"two-dimensional":[10,47],"non-linear":[11,50,87],"singular":[12,86],"Volterra":[13],"integral":[14,51,88],"equations":[15,42],"with":[16,66,115],"fractional":[17,49],"orders":[18],"in":[19,82],"a":[20,44,91],"Banach":[21],"space":[22],"is":[23,43,97],"discussed":[24],"by":[25],"utilizing":[26],"concept":[28],"measure":[31],"non-compactness":[33],"fixed-point":[35],"theorem.":[36],"fact,":[38],"kind":[40],"generalization":[45],"Riemann-Liouville":[48],"equations.":[52,89],"To":[53,72],"approximate":[54],"above":[59],"problem,":[60],"we":[61,78],"use":[62],"modified":[63],"homotopy":[64],"perturbation":[65],"help":[68],"Adomian":[70],"polynomials.":[71],"validity":[73],"derived":[76],"results,":[77],"introduce":[79],"an":[80],"example":[81,96],"field":[84],"Hence,":[90],"semianalytic":[92],"given":[95],"obtained":[98],"ensuring":[99],"satisfactory":[100],"accuracy.":[101],"Also,":[102],"to":[103],"ensure":[104],"effectiveness":[106],"proposed":[109],"method":[110],"results":[112],"are":[113],"compared":[114],"some":[116],"other":[117],"works.":[118]},"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2026-06-18T00:00:00"}
