{"id":"https://openalex.org/W2909045203","doi":"https://doi.org/10.1007/s11075-019-00654-5","title":"Identification of the time-dependent source term in a multi-term time-fractional diffusion equation","display_name":"Identification of the time-dependent source term in a multi-term time-fractional diffusion equation","publication_year":2019,"publication_date":"2019-01-12","ids":{"openalex":"https://openalex.org/W2909045203","doi":"https://doi.org/10.1007/s11075-019-00654-5","mag":"2909045203"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-019-00654-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00654-5","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/A5049976931","display_name":"Y. S. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4210125346","display_name":"Gansu Institute of Political Science and Law","ror":"https://ror.org/025km4h87","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125346"]},{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]},{"id":"https://openalex.org/I16295237","display_name":"Gansu Agricultural University","ror":"https://ror.org/05ym42410","country_code":"CN","type":"education","lineage":["https://openalex.org/I16295237"]},{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]},{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Y. S. Li","raw_affiliation_strings":["School of Cyber Security, Gansu Institute of Political Science and Law, Lanzhou, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","School of Cyber Security, Gansu Institute of Political Science and Law, Lanzhou, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Cyber Security, Gansu Institute of Political Science and Law, Lanzhou, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210125346"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153","https://openalex.org/I22716506","https://openalex.org/I16295237"]},{"raw_affiliation_string":"School of Cyber Security, Gansu Institute of Political Science and Law, Lanzhou, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210125346"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031744596","display_name":"Liangliang Sun","orcid":"https://orcid.org/0000-0002-4183-4058"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]},{"id":"https://openalex.org/I16295237","display_name":"Gansu Agricultural University","ror":"https://ror.org/05ym42410","country_code":"CN","type":"education","lineage":["https://openalex.org/I16295237"]},{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]},{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"L. L. Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153","https://openalex.org/I22716506","https://openalex.org/I16295237"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078479291","display_name":"Z.Q. Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]},{"id":"https://openalex.org/I16295237","display_name":"Gansu Agricultural University","ror":"https://ror.org/05ym42410","country_code":"CN","type":"education","lineage":["https://openalex.org/I16295237"]},{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]},{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Q. Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153","https://openalex.org/I22716506","https://openalex.org/I16295237"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210152533"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085753115","display_name":"Ting Wei","orcid":"https://orcid.org/0000-0001-6058-6806"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]},{"id":"https://openalex.org/I4210152533","display_name":"Lanzhou University of Finance and Economics","ror":"https://ror.org/04v7yv031","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152533"]},{"id":"https://openalex.org/I16295237","display_name":"Gansu Agricultural University","ror":"https://ror.org/05ym42410","country_code":"CN","type":"education","lineage":["https://openalex.org/I16295237"]},{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"T. Wei","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153","https://openalex.org/I22716506","https://openalex.org/I16295237"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210152533"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085753115"],"corresponding_institution_ids":["https://openalex.org/I16295237","https://openalex.org/I22716506","https://openalex.org/I4210152533","https://openalex.org/I76214153"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.2444,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.77738462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"82","issue":"4","first_page":"1279","last_page":"1301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7202725410461426},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7160375118255615},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6263420581817627},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6229170560836792},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5995870232582092},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.54981529712677},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5465001463890076},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5033103823661804},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4888117015361786},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47626063227653503},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.43547338247299194},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43376174569129944},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4164983332157135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15753880143165588},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11531504988670349},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07360237836837769}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7202725410461426},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7160375118255615},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6263420581817627},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6229170560836792},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5995870232582092},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.54981529712677},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5465001463890076},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5033103823661804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4888117015361786},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47626063227653503},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.43547338247299194},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43376174569129944},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4164983332157135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15753880143165588},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11531504988670349},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07360237836837769},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-019-00654-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-019-00654-5","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"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/371175","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/371175","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/418720","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/418720","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","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":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1020918943","display_name":null,"funder_award_id":"11601207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3092123571","display_name":null,"funder_award_id":"11371181","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6700717588","display_name":null,"funder_award_id":"11771192","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W200132056","https://openalex.org/W582587363","https://openalex.org/W588998842","https://openalex.org/W1529838443","https://openalex.org/W1545761024","https://openalex.org/W1570089119","https://openalex.org/W1571391776","https://openalex.org/W1578255497","https://openalex.org/W1853203691","https://openalex.org/W1969547415","https://openalex.org/W1981334702","https://openalex.org/W1986713454","https://openalex.org/W1992429301","https://openalex.org/W1998312161","https://openalex.org/W2004097100","https://openalex.org/W2006281429","https://openalex.org/W2016124038","https://openalex.org/W2021492437","https://openalex.org/W2027205768","https://openalex.org/W2033102362","https://openalex.org/W2033402214","https://openalex.org/W2034401440","https://openalex.org/W2048865131","https://openalex.org/W2051245043","https://openalex.org/W2060240831","https://openalex.org/W2060650941","https://openalex.org/W2066060749","https://openalex.org/W2073686786","https://openalex.org/W2081811871","https://openalex.org/W2091313463","https://openalex.org/W2111271983","https://openalex.org/W2144458158","https://openalex.org/W2215263022","https://openalex.org/W2397817385","https://openalex.org/W2420651851","https://openalex.org/W2493177303","https://openalex.org/W2500538847","https://openalex.org/W2586401190","https://openalex.org/W2757446537","https://openalex.org/W2995974282","https://openalex.org/W3044006004","https://openalex.org/W3100087909","https://openalex.org/W4231391020","https://openalex.org/W4245698330","https://openalex.org/W4285719527","https://openalex.org/W6606165372"],"related_works":["https://openalex.org/W3131586246","https://openalex.org/W4232854940","https://openalex.org/W2028208404","https://openalex.org/W2004501529","https://openalex.org/W4298516010","https://openalex.org/W2793340545","https://openalex.org/W1974122505","https://openalex.org/W2967187965","https://openalex.org/W2996388602","https://openalex.org/W2080556621"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}