{"id":"https://openalex.org/W4200000747","doi":"https://doi.org/10.5269/bspm.45265","title":"An inverse source problem for a two terms time-fractional diffusion equation","display_name":"An inverse source problem for a two terms time-fractional diffusion equation","publication_year":2021,"publication_date":"2021-12-17","ids":{"openalex":"https://openalex.org/W4200000747","doi":"https://doi.org/10.5269/bspm.45265"},"language":"en","primary_location":{"id":"doi:10.5269/bspm.45265","doi":"https://doi.org/10.5269/bspm.45265","is_oa":true,"landing_page_url":"https://doi.org/10.5269/bspm.45265","pdf_url":null,"source":{"id":"https://openalex.org/S4210185623","display_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","issn_l":"0037-8712","issn":["0037-8712","2175-1188"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312547","host_organization_name":"Sociedade Brasileira de Matem\u00e1tica","host_organization_lineage":["https://openalex.org/P4310312547"],"host_organization_lineage_names":["Sociedade Brasileira de Matem\u00e1tica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.5269/bspm.45265","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072840013","display_name":"Fatima Dib","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fatima Dib","raw_affiliation_strings":["Superior school of applied sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Superior school of applied sciences","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069904706","display_name":"Mokhtar Kirane","orcid":"https://orcid.org/0000-0002-4867-7542","observed_orcids":["https://orcid.org/0000-0002-4867-7542","https://orcid.org/0000-0003-2221-9778","https://orcid.org/0009-0003-7992-1987"]},"institutions":[{"id":"https://openalex.org/I78744979","display_name":"La Rochelle Universit\u00e9","ror":"https://ror.org/04mv1z119","country_code":"FR","type":"education","lineage":["https://openalex.org/I78744979"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mokhtar Kirane","raw_affiliation_strings":["Universit\u00e9 de La Rochelle"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de La Rochelle","institution_ids":["https://openalex.org/I78744979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2599,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78083088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"40","issue":null,"first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.3865000009536743,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.3865000009536743,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.36469998955726624,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.21699999272823334,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/inverse-source-problem","display_name":"inverse source problem","score":1.0},{"id":"https://openalex.org/keywords/time-fractional-diffusion-equation","display_name":"time-fractional diffusion equation","score":0.9319999814033508},{"id":"https://openalex.org/keywords/nonlocal-boundary-conditions","display_name":"nonlocal boundary conditions","score":0.8510000109672546},{"id":"https://openalex.org/keywords/source-term-identification","display_name":"source term identification","score":0.5649999976158142},{"id":"https://openalex.org/keywords/temperature-distribution","display_name":"temperature distribution","score":0.5830000042915344}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6429433822631836},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.597735583782196},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.591519296169281},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5838661789894104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5807408094406128},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5479152798652649},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5399072766304016},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4833390414714813},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48164597153663635},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.47133564949035645},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4708753824234009},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4373834431171417},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41104578971862793},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19459733366966248},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08802959322929382},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.081758052110672},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5269/bspm.45265","doi":"https://doi.org/10.5269/bspm.45265","is_oa":true,"landing_page_url":"https://doi.org/10.5269/bspm.45265","pdf_url":null,"source":{"id":"https://openalex.org/S4210185623","display_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","issn_l":"0037-8712","issn":["0037-8712","2175-1188"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312547","host_organization_name":"Sociedade Brasileira de Matem\u00e1tica","host_organization_lineage":["https://openalex.org/P4310312547"],"host_organization_lineage_names":["Sociedade Brasileira de Matem\u00e1tica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.5269/bspm.45265","doi":"https://doi.org/10.5269/bspm.45265","is_oa":true,"landing_page_url":"https://doi.org/10.5269/bspm.45265","pdf_url":null,"source":{"id":"https://openalex.org/S4210185623","display_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","issn_l":"0037-8712","issn":["0037-8712","2175-1188"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310312547","host_organization_name":"Sociedade Brasileira de Matem\u00e1tica","host_organization_lineage":["https://openalex.org/P4310312547"],"host_organization_lineage_names":["Sociedade Brasileira de Matem\u00e1tica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boletim da Sociedade Paranaense de Matem\u00e1tica","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1853203691","https://openalex.org/W1970415809","https://openalex.org/W1977023522","https://openalex.org/W2063108965","https://openalex.org/W2066060749","https://openalex.org/W2068703762","https://openalex.org/W2073686786","https://openalex.org/W2083197540"],"related_works":["https://openalex.org/W4392742076","https://openalex.org/W4394952511","https://openalex.org/W2158356954","https://openalex.org/W2181344213","https://openalex.org/W4417453262","https://openalex.org/W2750517081","https://openalex.org/W4392640296","https://openalex.org/W2211069905","https://openalex.org/W2468844625","https://openalex.org/W2551793888"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"an":[5,38],"inverse":[6],"problem":[7],"for":[8],"a":[9,19,25],"linear":[10],"heat":[11],"equation":[12],"involving":[13],"two":[14],"time-fractional":[15],"derivatives,":[16],"subject":[17],"to":[18],"nonlocal":[20],"boundary":[21],"condition.":[22],"We":[23],"determine":[24],"source":[26],"term":[27],"independent":[28],"of":[29,42],"the":[30,34],"space":[31],"variable,":[32],"and":[33],"temperature":[35],"distribution":[36],"with":[37],"over-":[39],"determining":[40],"function":[41],"integral":[43],"type.":[44]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2021-12-31T00:00:00"}