{"id":"https://openalex.org/W2914570832","doi":"https://doi.org/10.1515/cmam-2018-0194","title":"Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data","display_name":"Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data","publication_year":2019,"publication_date":"2019-01-20","ids":{"openalex":"https://openalex.org/W2914570832","doi":"https://doi.org/10.1515/cmam-2018-0194","mag":"2914570832"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0194","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0194","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5033545588","display_name":"Suzhen Jiang","orcid":"https://orcid.org/0000-0002-0718-5592"},"institutions":[{"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":"Suzhen Jiang","raw_affiliation_strings":["School of Mathematics and Statistics , Lanzhou University , Gansu 730000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Lanzhou University , Gansu 730000 , P. R. China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031532351","display_name":"Kaifang Liao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117164","display_name":"Luoyang Normal University","ror":"https://ror.org/029man787","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117164"]},{"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":"Kaifang Liao","raw_affiliation_strings":["School of Mathematics and Statistics , Lanzhou University , Gansu 730000 ; and Department of Mathematics, Luoyang Normal University, Henan 471934 P. R. China","School of Mathematics and Statistics, Lanzhou University, Gansu 730000"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Lanzhou University , Gansu 730000 ; and Department of Mathematics, Luoyang Normal University, Henan 471934 P. R. China","institution_ids":["https://openalex.org/I4210117164","https://openalex.org/I76214153"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Gansu 730000","institution_ids":["https://openalex.org/I76214153"]}]},{"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/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":"Ting Wei","raw_affiliation_strings":["School of Mathematics and Statistics , Lanzhou University , Gansu 730000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Lanzhou University , Gansu 730000 , P. R. China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085753115"],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":null,"apc_paid":null,"fwci":0.3307,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.535623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"1","first_page":"109","last_page":"120"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9954000115394592,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7783817648887634},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6714091300964355},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6299142241477966},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.604232907295227},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5628857016563416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5580118298530579},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5456576347351074},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.49989819526672363},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.49331799149513245},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4873712658882141},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.45904725790023804},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.44531235098838806},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.42988157272338867},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.42871612310409546},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4205891489982605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11643493175506592},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08126798272132874}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7783817648887634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6714091300964355},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6299142241477966},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.604232907295227},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5628857016563416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5580118298530579},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5456576347351074},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.49989819526672363},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.49331799149513245},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4873712658882141},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.45904725790023804},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.44531235098838806},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.42988157272338867},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.42871612310409546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4205891489982605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11643493175506592},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08126798272132874},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1515/cmam-2018-0194","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0194","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/418833","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/418833","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/:262010/437775","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/437775","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":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/443910","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/443910","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":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/371290","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/371290","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/:262010/430798","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/430798","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":"\u671f\u520a\u8bba\u6587"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"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"},{"id":"https://openalex.org/G7982997291","display_name":null,"funder_award_id":"11601216","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":34,"referenced_works":["https://openalex.org/W171286733","https://openalex.org/W1520042376","https://openalex.org/W1570089119","https://openalex.org/W1584611818","https://openalex.org/W1963843024","https://openalex.org/W1969631463","https://openalex.org/W1986713454","https://openalex.org/W1987191262","https://openalex.org/W1998454237","https://openalex.org/W2016680653","https://openalex.org/W2018183327","https://openalex.org/W2018207223","https://openalex.org/W2018207569","https://openalex.org/W2033102362","https://openalex.org/W2033402214","https://openalex.org/W2041540906","https://openalex.org/W2046631971","https://openalex.org/W2047594597","https://openalex.org/W2062802638","https://openalex.org/W2065201216","https://openalex.org/W2091714479","https://openalex.org/W2144458158","https://openalex.org/W2161618617","https://openalex.org/W2230775999","https://openalex.org/W2319377454","https://openalex.org/W2419048530","https://openalex.org/W2517843916","https://openalex.org/W2624731260","https://openalex.org/W2757446537","https://openalex.org/W2787959293","https://openalex.org/W2793231285","https://openalex.org/W2962999590","https://openalex.org/W4255895408","https://openalex.org/W6606836203"],"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/W2808609407","https://openalex.org/W4226289771","https://openalex.org/W2963341847","https://openalex.org/W2123573421","https://openalex.org/W2091887764"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"study,":[3],"we":[4],"consider":[5],"an":[6],"inverse":[7,31,47],"problem":[8,34,48,56],"of":[9,29,76],"recovering":[10],"the":[11,27,30,38,42,74,77],"initial":[12,32],"value":[13,33],"for":[14,72],"a":[15,53,59],"multi-dimensional":[16],"time-fractional":[17],"diffusion-wave":[18],"equation.":[19],"By":[20],"using":[21,58],"some":[22],"additional":[23],"boundary":[24],"measured":[25],"data,":[26],"uniqueness":[28],"is":[35,49],"proven":[36],"by":[37,57],"Laplace":[39],"transformation":[40],"and":[41,69],"analytic":[43],"continuation":[44],"technique.":[45],"The":[46],"formulated":[50],"to":[51],"solve":[52],"Tikhonov-type":[54],"optimization":[55],"finite-dimensional":[60],"approximation.":[61],"We":[62],"test":[63],"four":[64],"numerical":[65],"examples":[66],"in":[67],"one-dimensional":[68],"two-dimensional":[70],"cases":[71],"verifying":[73],"effectiveness":[75],"proposed":[78],"algorithm.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}