{"id":"https://openalex.org/W4387573071","doi":"https://doi.org/10.3390/axioms12100959","title":"Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation","display_name":"Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation","publication_year":2023,"publication_date":"2023-10-11","ids":{"openalex":"https://openalex.org/W4387573071","doi":"https://doi.org/10.3390/axioms12100959"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12100959","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12100959","pdf_url":"https://www.mdpi.com/2075-1680/12/10/959/pdf?version=1697091045","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/10/959/pdf?version=1697091045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033923340","display_name":"Fangfang Wu","orcid":"https://orcid.org/0000-0003-0592-0474"},"institutions":[{"id":"https://openalex.org/I157507598","display_name":"Shenyang University of Technology","ror":"https://ror.org/00d7f8730","country_code":"CN","type":"education","lineage":["https://openalex.org/I157507598"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fangfang Wu","raw_affiliation_strings":["College of Science, Shenyang University of Technology, Shenyang 110870, China"],"raw_orcid":"https://orcid.org/0000-0003-0592-0474","affiliations":[{"raw_affiliation_string":"College of Science, Shenyang University of Technology, Shenyang 110870, China","institution_ids":["https://openalex.org/I157507598"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101255070","display_name":"Chuangui Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I157507598","display_name":"Shenyang University of Technology","ror":"https://ror.org/00d7f8730","country_code":"CN","type":"education","lineage":["https://openalex.org/I157507598"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuangui Lu","raw_affiliation_strings":["College of Science, Shenyang University of Technology, Shenyang 110870, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shenyang University of Technology, Shenyang 110870, China","institution_ids":["https://openalex.org/I157507598"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100381041","display_name":"Yingying Wang","orcid":"https://orcid.org/0009-0006-8531-5635"},"institutions":[{"id":"https://openalex.org/I157507598","display_name":"Shenyang University of Technology","ror":"https://ror.org/00d7f8730","country_code":"CN","type":"education","lineage":["https://openalex.org/I157507598"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingying Wang","raw_affiliation_strings":["College of Science, Shenyang University of Technology, Shenyang 110870, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shenyang University of Technology, Shenyang 110870, China","institution_ids":["https://openalex.org/I157507598"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025389890","display_name":"Na Hu","orcid":"https://orcid.org/0000-0003-1656-0101"},"institutions":[{"id":"https://openalex.org/I157507598","display_name":"Shenyang University of Technology","ror":"https://ror.org/00d7f8730","country_code":"CN","type":"education","lineage":["https://openalex.org/I157507598"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Na Hu","raw_affiliation_strings":["College of Science, Shenyang University of Technology, Shenyang 110870, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shenyang University of Technology, Shenyang 110870, China","institution_ids":["https://openalex.org/I157507598"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033923340"],"corresponding_institution_ids":["https://openalex.org/I157507598"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.6026,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62349569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"10","first_page":"959","last_page":"959"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9993000030517578,"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.992900013923645,"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":0.7464860081672668},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7201833724975586},{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.7164549827575684},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7089055776596069},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.6181021332740784},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5223632454872131},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5123473405838013},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5070126056671143},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.49858975410461426},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4960525929927826},{"id":"https://openalex.org/keywords/hpp-model","display_name":"HPP model","score":0.46144288778305054},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46018701791763306},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4477444291114807},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4462757706642151},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14517059922218323}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7464860081672668},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7201833724975586},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.7164549827575684},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7089055776596069},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.6181021332740784},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5223632454872131},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5123473405838013},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5070126056671143},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.49858975410461426},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4960525929927826},{"id":"https://openalex.org/C67906445","wikidata":"https://www.wikidata.org/wiki/Q17027724","display_name":"HPP model","level":4,"score":0.46144288778305054},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46018701791763306},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4477444291114807},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4462757706642151},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14517059922218323},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12100959","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12100959","pdf_url":"https://www.mdpi.com/2075-1680/12/10/959/pdf?version=1697091045","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0fcb5d64bc1e49d68c7dd7dc60ef1a30","is_oa":true,"landing_page_url":"https://doaj.org/article/0fcb5d64bc1e49d68c7dd7dc60ef1a30","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 10, p 959 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12100959","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12100959","pdf_url":"https://www.mdpi.com/2075-1680/12/10/959/pdf?version=1697091045","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G602965012","display_name":null,"funder_award_id":"62103289","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8892620237","display_name":null,"funder_award_id":"LJKMZ20220485","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":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387573071.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W140154881","https://openalex.org/W1502589723","https://openalex.org/W1504271241","https://openalex.org/W1969312973","https://openalex.org/W1973950856","https://openalex.org/W1993609521","https://openalex.org/W1997926500","https://openalex.org/W1999295855","https://openalex.org/W2006830600","https://openalex.org/W2008474712","https://openalex.org/W2030146312","https://openalex.org/W2033593438","https://openalex.org/W2035157815","https://openalex.org/W2035927295","https://openalex.org/W2036215498","https://openalex.org/W2037606505","https://openalex.org/W2041835548","https://openalex.org/W2052929127","https://openalex.org/W2063052480","https://openalex.org/W2064672711","https://openalex.org/W2079949023","https://openalex.org/W2082280299","https://openalex.org/W2090231693","https://openalex.org/W2116807840","https://openalex.org/W2117242079","https://openalex.org/W2133301037","https://openalex.org/W2133374930","https://openalex.org/W2167970717","https://openalex.org/W2907331802","https://openalex.org/W2941705112","https://openalex.org/W3040330965","https://openalex.org/W3111152365","https://openalex.org/W4211052487","https://openalex.org/W4225843936","https://openalex.org/W4247953052","https://openalex.org/W4280501108","https://openalex.org/W4292737345","https://openalex.org/W4315701285","https://openalex.org/W4324361284","https://openalex.org/W4327971534","https://openalex.org/W4385420692","https://openalex.org/W6629971914","https://openalex.org/W6643640137","https://openalex.org/W6757296410","https://openalex.org/W6761540273"],"related_works":["https://openalex.org/W2411948770","https://openalex.org/W2091687378","https://openalex.org/W2026659976","https://openalex.org/W2083059313","https://openalex.org/W1600706040","https://openalex.org/W155120597","https://openalex.org/W2062900651","https://openalex.org/W2289107462","https://openalex.org/W2374711637","https://openalex.org/W2002628205"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,74,99],"concerned":[3],"with":[4,46,70,88],"the":[5,21,26,29,56,63,67,81,93,96,102],"lattice":[6],"Boltzmann":[7],"(LB)":[8],"method":[9],"for":[10],"a":[11],"class":[12],"of":[13,28,95],"time":[14],"fractional":[15],"partial":[16,43],"differential":[17,44],"equations":[18,45],"(FPDEs)":[19],"in":[20,34,61,85],"Caputo":[22,30],"sense.":[23],"By":[24],"utilizing":[25],"properties":[27],"derivative":[31],"and":[32,91],"discretization":[33],"time,":[35],"FPDEs":[36],"can":[37],"be":[38],"approximately":[39],"transformed":[40],"into":[41,55],"standard":[42],"integer":[47],"orders.":[48],"Through":[49],"incorporating":[50],"an":[51],"auxiliary":[52],"distribution":[53],"function":[54],"evolution":[57],"equation,":[58],"which":[59],"assists":[60],"recovering":[62],"macroscopic":[64],"quantity":[65],"u,":[66],"LB":[68],"model":[69,98],"spatial":[71],"second-order":[72],"accuracy":[73,94],"constructed.":[75],"The":[76],"numerical":[77,82],"experiments":[78],"verify":[79],"that":[80,92],"results":[83],"are":[84],"good":[86],"agreement":[87],"analytical":[89],"solutions":[90],"present":[97],"better":[100],"than":[101],"previous":[103],"solutions.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}