{"id":"https://openalex.org/W4286209817","doi":"https://doi.org/10.3390/e24071002","title":"Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact","display_name":"Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact","publication_year":2022,"publication_date":"2022-07-20","ids":{"openalex":"https://openalex.org/W4286209817","doi":"https://doi.org/10.3390/e24071002","pmid":"https://pubmed.ncbi.nlm.nih.gov/35885225"},"language":"en","primary_location":{"id":"doi:10.3390/e24071002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24071002","pdf_url":"https://www.mdpi.com/1099-4300/24/7/1002/pdf?version=1658294068","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/7/1002/pdf?version=1658294068","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":["Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. 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 Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 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":0.2622,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.444749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"24","issue":"7","first_page":"1002","last_page":"1002"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9998999834060669,"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":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9891999959945679,"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/mathematical-analysis","display_name":"Mathematical analysis","score":0.6207413077354431},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.6172456741333008},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.6015057563781738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5841354131698608},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5687126517295837},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.5554378032684326},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5443482398986816},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5116174817085266},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.467649906873703},{"id":"https://openalex.org/keywords/absorption","display_name":"Absorption (acoustics)","score":0.4674355089664459},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4594520032405853},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43205544352531433},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4193708896636963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27507421374320984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14876431226730347},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12777265906333923},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06212043762207031},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.057662636041641235}],"concepts":[{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6207413077354431},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6172456741333008},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.6015057563781738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5841354131698608},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5687126517295837},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.5554378032684326},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5443482398986816},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5116174817085266},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.467649906873703},{"id":"https://openalex.org/C125287762","wikidata":"https://www.wikidata.org/wiki/Q1758948","display_name":"Absorption (acoustics)","level":2,"score":0.4674355089664459},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4594520032405853},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43205544352531433},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4193708896636963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27507421374320984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14876431226730347},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12777265906333923},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06212043762207031},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.057662636041641235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24071002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24071002","pdf_url":"https://www.mdpi.com/1099-4300/24/7/1002/pdf?version=1658294068","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:35885225","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35885225","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:dd837dac33444ec1bbc2f6413dd65da8","is_oa":true,"landing_page_url":"https://doaj.org/article/dd837dac33444ec1bbc2f6413dd65da8","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 7, p 1002 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/7/1002/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24071002","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 7; Pages: 1002","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9315876","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9315876","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24071002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24071002","pdf_url":"https://www.mdpi.com/1099-4300/24/7/1002/pdf?version=1658294068","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4286209817.pdf","grobid_xml":"https://content.openalex.org/works/W4286209817.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W144919191","https://openalex.org/W1633315028","https://openalex.org/W1948181060","https://openalex.org/W1972551677","https://openalex.org/W1983026806","https://openalex.org/W1983705302","https://openalex.org/W1992124855","https://openalex.org/W1993230642","https://openalex.org/W2011281900","https://openalex.org/W2038000836","https://openalex.org/W2048626366","https://openalex.org/W2051877487","https://openalex.org/W2084535841","https://openalex.org/W2099179152","https://openalex.org/W2140890153","https://openalex.org/W2291960678","https://openalex.org/W2486112781","https://openalex.org/W2522334816","https://openalex.org/W2796779111","https://openalex.org/W2946178965","https://openalex.org/W2990946391","https://openalex.org/W3004295606","https://openalex.org/W3187784755","https://openalex.org/W4205457643","https://openalex.org/W4229641655","https://openalex.org/W4236165936","https://openalex.org/W4238174032","https://openalex.org/W4239526824","https://openalex.org/W4240384253","https://openalex.org/W4242247520","https://openalex.org/W4247877478"],"related_works":["https://openalex.org/W2389517732","https://openalex.org/W4213231742","https://openalex.org/W346881876","https://openalex.org/W2084108921","https://openalex.org/W4388240777","https://openalex.org/W2607759403","https://openalex.org/W2066116605","https://openalex.org/W2106562951","https://openalex.org/W281041820","https://openalex.org/W4308910509"],"abstract_inverted_index":{"The":[0,19,28,63,69],"axisymmetric":[1],"time-fractional":[2,36],"diffusion":[3],"equation":[4,30,41],"with":[5],"mass":[6],"absorption":[7],"is":[8,26,67],"studied":[9],"in":[10],"a":[11],"circle":[12],"under":[13],"the":[14,23,35,39,43,49,55,81],"time-harmonic":[15],"Dirichlet":[16],"boundary":[17],"condition.":[18],"Caputo":[20],"derivative":[21],"of":[22,38,48,54,71,80],"order":[24],"0<\u03b1\u22642":[25],"used.":[27],"investigated":[29],"can":[31],"be":[32],"considered":[33],"as":[34],"generalization":[37],"bioheat":[40],"and":[42,58],"Klein\u2212Gordon":[44],"equation.":[45],"Different":[46],"formulations":[47],"problem":[50],"for":[51,77],"integer":[52],"values":[53,79],"time-derivatives":[56],"\u03b1=1":[57],"\u03b1=2":[59],"are":[60,74],"also":[61],"discussed.":[62],"integral":[64],"transform":[65],"technique":[66],"employed.":[68],"outcomes":[70],"numerical":[72],"calculations":[73],"illustrated":[75],"graphically":[76],"different":[78],"parameters.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}