{"id":"https://openalex.org/W4313332575","doi":"https://doi.org/10.1080/00207160.2022.2163588","title":"Numerical method for solving the fractional evolutionary model of bi-flux diffusion processes","display_name":"Numerical method for solving the fractional evolutionary model of bi-flux diffusion processes","publication_year":2022,"publication_date":"2022-12-29","ids":{"openalex":"https://openalex.org/W4313332575","doi":"https://doi.org/10.1080/00207160.2022.2163588"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2163588","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2163588","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5013439637","display_name":"Cui-cui Ji","orcid":"https://orcid.org/0000-0003-2855-9378"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cui-Cui Ji","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042219520","display_name":"Wenzhen Qu","orcid":"https://orcid.org/0000-0003-3591-4593"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenzhen Qu","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108662809","display_name":"Maosheng Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maosheng Jiang","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao, People's Republic of China","institution_ids":["https://openalex.org/I108688024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013439637"],"corresponding_institution_ids":["https://openalex.org/I108688024"],"apc_list":null,"apc_paid":null,"fwci":0.5479,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61695272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"100","issue":"4","first_page":"880","last_page":"900"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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":0.7421865463256836},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6060925722122192},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5810338258743286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5333364605903625},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.5064154863357544},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5023062229156494},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4952494204044342},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.49037814140319824},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4444538652896881},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3631311058998108},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10839346051216125},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09384775161743164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7421865463256836},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6060925722122192},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5810338258743286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5333364605903625},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.5064154863357544},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5023062229156494},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4952494204044342},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.49037814140319824},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4444538652896881},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3631311058998108},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10839346051216125},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09384775161743164},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2163588","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2163588","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8399999737739563,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1443038236","display_name":null,"funder_award_id":"ZR2020QA033, ZR2021MA072","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2250699681","display_name":null,"funder_award_id":"12001307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8417687472","display_name":null,"funder_award_id":"ZR2021QA018","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W374977727","https://openalex.org/W582922657","https://openalex.org/W1528987510","https://openalex.org/W1584611818","https://openalex.org/W1762244538","https://openalex.org/W1980593821","https://openalex.org/W1984237658","https://openalex.org/W1991982189","https://openalex.org/W2013812365","https://openalex.org/W2015550173","https://openalex.org/W2019324632","https://openalex.org/W2030146312","https://openalex.org/W2043080303","https://openalex.org/W2049520374","https://openalex.org/W2053256951","https://openalex.org/W2054311040","https://openalex.org/W2062650267","https://openalex.org/W2064361774","https://openalex.org/W2065232540","https://openalex.org/W2070505112","https://openalex.org/W2073659542","https://openalex.org/W2084142728","https://openalex.org/W2094838226","https://openalex.org/W2111271983","https://openalex.org/W2140057174","https://openalex.org/W2165076033","https://openalex.org/W2201614421","https://openalex.org/W2589656637","https://openalex.org/W2601627861","https://openalex.org/W2608656286","https://openalex.org/W2787959293","https://openalex.org/W2799821673","https://openalex.org/W2801192398","https://openalex.org/W2883517678","https://openalex.org/W2979336221","https://openalex.org/W2990575151","https://openalex.org/W3028010004","https://openalex.org/W3106441075","https://openalex.org/W3118368751","https://openalex.org/W3125882716","https://openalex.org/W3127312276","https://openalex.org/W3134665841","https://openalex.org/W3139348098","https://openalex.org/W3155529219","https://openalex.org/W3197789521","https://openalex.org/W3199189009","https://openalex.org/W4205326049","https://openalex.org/W4206782663","https://openalex.org/W4212851635","https://openalex.org/W4231695981","https://openalex.org/W4244854774","https://openalex.org/W4247877478","https://openalex.org/W4253243291","https://openalex.org/W4297535500","https://openalex.org/W4306804937","https://openalex.org/W4307295572"],"related_works":["https://openalex.org/W4213231742","https://openalex.org/W2066116605","https://openalex.org/W2161513111","https://openalex.org/W912076904","https://openalex.org/W2030146312","https://openalex.org/W3164740183","https://openalex.org/W2525556503","https://openalex.org/W3125365929","https://openalex.org/W2011648757","https://openalex.org/W2509889981"],"abstract_inverted_index":{"In":[0,51],"this":[1],"paper,":[2],"based":[3],"on":[4],"the":[5,17,23,30,48,56,62,66],"nonuniform":[6],"time":[7],"meshes,":[8],"we":[9,26],"proposed":[10],"an":[11],"efficient":[12],"difference":[13],"scheme":[14,32],"for":[15],"solving":[16],"time-fractional":[18],"bi-flux":[19],"diffusion":[20,63],"equation.":[21],"By":[22],"energy":[24],"method,":[25],"then":[27],"proved":[28],"that":[29],"present":[31],"is":[33],"unconditionally":[34],"stable":[35],"and":[36],"convergent":[37],"in":[38],"L2":[39],"norm.":[40],"Several":[41],"numerical":[42,53],"examples":[43],"are":[44],"given":[45],"to":[46],"verify":[47],"theoretical":[49],"results.":[50],"addition,":[52],"simulations":[54],"show":[55],"order":[57],"of":[58,65],"fractional":[59],"derivative":[60],"affects":[61],"rate":[64],"particles.":[67]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
