{"id":"https://openalex.org/W4402612427","doi":"https://doi.org/10.1137/24m1631614","title":"Some Gr\u00f6nwall Inequalities for a Class of Discretizations of Time Fractional Equations on Nonuniform Meshes","display_name":"Some Gr\u00f6nwall Inequalities for a Class of Discretizations of Time Fractional Equations on Nonuniform Meshes","publication_year":2024,"publication_date":"2024-09-18","ids":{"openalex":"https://openalex.org/W4402612427","doi":"https://doi.org/10.1137/24m1631614"},"language":"en","primary_location":{"id":"doi:10.1137/24m1631614","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1631614","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5104001258","display_name":"Yuanyuan Feng","orcid":"https://orcid.org/0000-0001-6873-6274"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuanyuan Feng","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100440225","display_name":"Lei Li","orcid":"https://orcid.org/0000-0001-5304-8380"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Lei Li","raw_affiliation_strings":["Corresponding author.\u00a0School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China"],"raw_orcid":"https://orcid.org/0000-0001-5304-8380","affiliations":[{"raw_affiliation_string":"Corresponding author.\u00a0School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China","institution_ids":["https://openalex.org/I4210158445"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028504471","display_name":"Jianguo Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Guo Liu","raw_affiliation_strings":["Department of Mathematics, Department of Physics, Duke University, Durham, NC 27708 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Department of Physics, Duke University, Durham, NC 27708 USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058967726","display_name":"Tao Tang","orcid":"https://orcid.org/0000-0003-2919-2774"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Tang","raw_affiliation_strings":["School of Electrical and Computer Engineering, Guangzhou Nanfang College, Guangzhou 510970, China and Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai, 519087, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Guangzhou Nanfang College, Guangzhou 510970, China and Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College, Zhuhai, 519087, China","institution_ids":["https://openalex.org/I12615008"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5104001258"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":1.141,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75879529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"62","issue":"5","first_page":"2196","last_page":"2221"},"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":0.9970999956130981,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8538941144943237},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7203123569488525},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6011813879013062},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.505394458770752},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.45204949378967285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3929069936275482},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16195666790008545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06569385528564453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8538941144943237},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7203123569488525},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6011813879013062},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.505394458770752},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.45204949378967285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3929069936275482},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16195666790008545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06569385528564453},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1631614","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1631614","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6100000143051147}],"awards":[{"id":"https://openalex.org/G1641394477","display_name":null,"funder_award_id":"K20911001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2621865199","display_name":null,"funder_award_id":"11731006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3523457993","display_name":null,"funder_award_id":"12301283","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4579902318","display_name":null,"funder_award_id":"2021YFA1002800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5980005209","display_name":null,"funder_award_id":"XDA25010403","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G6318382515","display_name":null,"funder_award_id":"2020YFA0712000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6871508810","display_name":null,"funder_award_id":"DMS-2106988","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7627071985","display_name":null,"funder_award_id":"12031013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8309809315","display_name":null,"funder_award_id":"12371400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8512854826","display_name":null,"funder_award_id":"TZ2018001","funder_id":"https://openalex.org/F4320336025","funder_display_name":"Science Challenge Project"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320336025","display_name":"Science Challenge Project","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1972645181","https://openalex.org/W2022622389","https://openalex.org/W2028525109","https://openalex.org/W2064361774","https://openalex.org/W2073659542","https://openalex.org/W2077560423","https://openalex.org/W2092173086","https://openalex.org/W2134837756","https://openalex.org/W2165076033","https://openalex.org/W2563245034","https://openalex.org/W2608656286","https://openalex.org/W2794616828","https://openalex.org/W2799821673","https://openalex.org/W2941043721","https://openalex.org/W2962847206","https://openalex.org/W2962972336","https://openalex.org/W2963377762","https://openalex.org/W2963408066","https://openalex.org/W2971817915","https://openalex.org/W2990575151","https://openalex.org/W3098333777","https://openalex.org/W3101707959","https://openalex.org/W3106441075","https://openalex.org/W3108780065","https://openalex.org/W3182314688","https://openalex.org/W4236865815","https://openalex.org/W4236893814","https://openalex.org/W4247953052","https://openalex.org/W4295788733","https://openalex.org/W4387246044","https://openalex.org/W4389134605","https://openalex.org/W4399676311"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2087496541","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2085564391","https://openalex.org/W1984758362","https://openalex.org/W2042049060","https://openalex.org/W2992936613","https://openalex.org/W2108615321"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-27T08:22:11.395708","created_date":"2025-10-10T00:00:00"}