{"id":"https://openalex.org/W2946638711","doi":"https://doi.org/10.3390/sym11050689","title":"Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading","display_name":"Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading","publication_year":2019,"publication_date":"2019-05-18","ids":{"openalex":"https://openalex.org/W2946638711","doi":"https://doi.org/10.3390/sym11050689","mag":"2946638711"},"language":"en","primary_location":{"id":"doi:10.3390/sym11050689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050689","pdf_url":"https://www.mdpi.com/2073-8994/11/5/689/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/5/689/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090626156","display_name":"Yuriy Povstenko","orcid":"https://orcid.org/0000-0002-7492-5394"},"institutions":[{"id":"https://openalex.org/I126406834","display_name":"Jan D\u0142ugosz University","ror":"https://ror.org/0566yhn94","country_code":"PL","type":"education","lineage":["https://openalex.org/I126406834"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Yuriy Povstenko","raw_affiliation_strings":["Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland"],"affiliations":[{"raw_affiliation_string":"Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, Armii Krajowej 13/15, 42-200 Czestochowa, Poland","institution_ids":["https://openalex.org/I126406834"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086749225","display_name":"Tamara Kyrylych","orcid":"https://orcid.org/0000-0003-1630-7958"},"institutions":[{"id":"https://openalex.org/I126406834","display_name":"Jan D\u0142ugosz University","ror":"https://ror.org/0566yhn94","country_code":"PL","type":"education","lineage":["https://openalex.org/I126406834"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tamara Kyrylych","raw_affiliation_strings":["Department of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Zbierskiego 2/4, 42-200 Czestochowa, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Zbierskiego 2/4, 42-200 Czestochowa, Poland","institution_ids":["https://openalex.org/I126406834"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090626156"],"corresponding_institution_ids":["https://openalex.org/I126406834"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4446,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78250832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"5","first_page":"689","last_page":"689"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9997000098228455,"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":0.9937999844551086,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.7791961431503296},{"id":"https://openalex.org/keywords/heat-kernel","display_name":"Heat kernel","score":0.7563714981079102},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6354897618293762},{"id":"https://openalex.org/keywords/heat-flux","display_name":"Heat flux","score":0.6286400556564331},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5933778285980225},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.5900896787643433},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5835570693016052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5624755024909973},{"id":"https://openalex.org/keywords/relativistic-heat-conduction","display_name":"Relativistic heat conduction","score":0.5614888668060303},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5048109292984009},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.4193362891674042},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38879773020744324},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.30917567014694214},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2574256658554077},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2526560425758362},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.16931205987930298}],"concepts":[{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.7791961431503296},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.7563714981079102},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6354897618293762},{"id":"https://openalex.org/C159188206","wikidata":"https://www.wikidata.org/wiki/Q1478382","display_name":"Heat flux","level":3,"score":0.6286400556564331},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5933778285980225},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5900896787643433},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5835570693016052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5624755024909973},{"id":"https://openalex.org/C43818450","wikidata":"https://www.wikidata.org/wiki/Q7310828","display_name":"Relativistic heat conduction","level":4,"score":0.5614888668060303},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5048109292984009},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4193362891674042},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38879773020744324},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.30917567014694214},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2574256658554077},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2526560425758362},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16931205987930298}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11050689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050689","pdf_url":"https://www.mdpi.com/2073-8994/11/5/689/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9cfa96ad2f644856aabe97af906b22cb","is_oa":true,"landing_page_url":"https://doaj.org/article/9cfa96ad2f644856aabe97af906b22cb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 5, p 689 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11050689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11050689","pdf_url":"https://www.mdpi.com/2073-8994/11/5/689/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2946638711.pdf","grobid_xml":"https://content.openalex.org/works/W2946638711.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W144919191","https://openalex.org/W617206983","https://openalex.org/W1971070788","https://openalex.org/W1975570000","https://openalex.org/W1982045916","https://openalex.org/W1983026806","https://openalex.org/W1983705302","https://openalex.org/W1991567394","https://openalex.org/W1997579562","https://openalex.org/W2006682366","https://openalex.org/W2011970606","https://openalex.org/W2013388570","https://openalex.org/W2016755336","https://openalex.org/W2017385859","https://openalex.org/W2032521508","https://openalex.org/W2038000836","https://openalex.org/W2047911381","https://openalex.org/W2048626366","https://openalex.org/W2067748101","https://openalex.org/W2067855936","https://openalex.org/W2071593170","https://openalex.org/W2081531908","https://openalex.org/W2082901087","https://openalex.org/W2084535841","https://openalex.org/W2090007720","https://openalex.org/W2094244133","https://openalex.org/W2098432615","https://openalex.org/W2120370440","https://openalex.org/W2140890153","https://openalex.org/W2198979185","https://openalex.org/W2291960678","https://openalex.org/W2489930379","https://openalex.org/W2787959293","https://openalex.org/W2914463692","https://openalex.org/W2990946391","https://openalex.org/W4236165936","https://openalex.org/W4247877478","https://openalex.org/W4256340197","https://openalex.org/W6687369307"],"related_works":["https://openalex.org/W2032521508","https://openalex.org/W200417975","https://openalex.org/W2955151245","https://openalex.org/W2382732709","https://openalex.org/W2022722578","https://openalex.org/W1966385130","https://openalex.org/W2963145522","https://openalex.org/W2086387131","https://openalex.org/W1967381426","https://openalex.org/W2137684886"],"abstract_inverted_index":{"The":[0,27,55,61],"time-fractional":[1,28],"heat":[2,29,50],"conduction":[3,30],"equation":[4,31],"follows":[5],"from":[6],"the":[7,14,19,23,33,48,66,73],"law":[8,21],"of":[9,11,18,68,79],"conservation":[10],"energy":[12],"and":[13],"corresponding":[15],"time-nonlocal":[16],"extension":[17],"Fourier":[20],"with":[22,32,42,47,70],"\u201clong-tail\u201d":[24],"power":[25],"kernel.":[26],"Caputo":[34],"derivative":[35],"is":[36,59,63,82],"solved":[37],"for":[38],"an":[39],"infinite":[40],"plane":[41],"two":[43],"external":[44],"half-infinite":[45],"slits":[46],"prescribed":[49],"flux":[51],"across":[52],"their":[53],"surfaces.":[54],"integral":[56],"transform":[57],"technique":[58],"used.":[60],"solution":[62],"obtained":[64],"in":[65],"form":[67],"integrals":[69],"integrand":[71],"being":[72],"Mittag\u2013Leffler":[74],"function.":[75],"A":[76],"graphical":[77],"representation":[78],"numerical":[80],"results":[81],"given.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}