{"id":"https://openalex.org/W2690732668","doi":"https://doi.org/10.3390/e19070297","title":"Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation","display_name":"Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation","publication_year":2017,"publication_date":"2017-06-23","ids":{"openalex":"https://openalex.org/W2690732668","doi":"https://doi.org/10.3390/e19070297","mag":"2690732668"},"language":"en","primary_location":{"id":"doi:10.3390/e19070297","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070297","pdf_url":"https://www.mdpi.com/1099-4300/19/7/297/pdf?version=1498222730","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/7/297/pdf?version=1498222730","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"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Yuriy Povstenko","raw_affiliation_strings":["Institute of Mathematics and Computer Sciences, Faculty of Mathematical and Natural Sciences, Jan D\u0142ugosz University in Cz\u0229stochowa, al. Armii Krajowej 13/15, 42-200 Cz\u0229stochowa, Poland"],"raw_orcid":"https://orcid.org/0000-0002-7492-5394","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Sciences, Faculty of Mathematical and Natural Sciences, Jan D\u0142ugosz University in Cz\u0229stochowa, al. Armii Krajowej 13/15, 42-200 Cz\u0229stochowa, Poland","institution_ids":["https://openalex.org/I126406834","https://openalex.org/I4210137370"]}]},{"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":["Institute of Law, Administration and Management, Faculty of Philology and History, Jan D\u0142ugosz University in Cz\u0229stochowa, Zbierskiego 2/4, 42-200 Cz\u0229stochowa, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Law, Administration and Management, Faculty of Philology and History, Jan D\u0142ugosz University in Cz\u0229stochowa, Zbierskiego 2/4, 42-200 Cz\u0229stochowa, 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","https://openalex.org/I4210137370"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7697,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84632867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"7","first_page":"297","last_page":"297"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9962000250816345,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9879999756813049,"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":0.6984730958938599},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6906509399414062},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6748101711273193},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5608239769935608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5600571632385254},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5473485589027405},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5163077712059021},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5068629384040833},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4941387474536896},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"Fractional Laplacian","score":0.47278261184692383},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.46960505843162537},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4675261974334717},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4517133831977844},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4172464609146118},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41111573576927185},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36005449295043945},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13164126873016357},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08828923106193542}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6984730958938599},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6906509399414062},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6748101711273193},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5608239769935608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5600571632385254},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5473485589027405},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5163077712059021},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5068629384040833},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4941387474536896},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.47278261184692383},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46960505843162537},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4675261974334717},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4517133831977844},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4172464609146118},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41111573576927185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36005449295043945},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13164126873016357},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08828923106193542},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/e19070297","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070297","pdf_url":"https://www.mdpi.com/1099-4300/19/7/297/pdf?version=1498222730","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":"pmh:oai:mdpi.com:/1099-4300/19/7/297/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19070297","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 19; Issue 7; Pages: 297","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19070297","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070297","pdf_url":"https://www.mdpi.com/1099-4300/19/7/297/pdf?version=1498222730","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":[{"id":"https://openalex.org/F4320316157","display_name":"Uniwersytet Humanistyczno-Przyrodniczy im. Jana D\u0142ugosza w Cz\u0119stochowie","ror":"https://ror.org/0566yhn94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2690732668.pdf","grobid_xml":"https://content.openalex.org/works/W2690732668.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W144919191","https://openalex.org/W156131057","https://openalex.org/W1528987510","https://openalex.org/W1537785693","https://openalex.org/W1539707276","https://openalex.org/W1569585059","https://openalex.org/W1604162649","https://openalex.org/W1700684623","https://openalex.org/W1850511188","https://openalex.org/W1965265535","https://openalex.org/W1966793822","https://openalex.org/W1974234252","https://openalex.org/W1976417115","https://openalex.org/W1977360274","https://openalex.org/W1981956153","https://openalex.org/W1982121853","https://openalex.org/W1983026806","https://openalex.org/W1988571032","https://openalex.org/W1992026911","https://openalex.org/W1994770159","https://openalex.org/W1997347739","https://openalex.org/W2000339329","https://openalex.org/W2008474712","https://openalex.org/W2013668911","https://openalex.org/W2013812365","https://openalex.org/W2022987509","https://openalex.org/W2029301214","https://openalex.org/W2032213317","https://openalex.org/W2034472116","https://openalex.org/W2035203372","https://openalex.org/W2037973974","https://openalex.org/W2040726100","https://openalex.org/W2041468391","https://openalex.org/W2045514685","https://openalex.org/W2048626366","https://openalex.org/W2055922934","https://openalex.org/W2065213885","https://openalex.org/W2065647211","https://openalex.org/W2066053624","https://openalex.org/W2071945239","https://openalex.org/W2083314770","https://openalex.org/W2084535841","https://openalex.org/W2092618061","https://openalex.org/W2095171236","https://openalex.org/W2099111135","https://openalex.org/W2107162131","https://openalex.org/W2111072798","https://openalex.org/W2111271983","https://openalex.org/W2120217909","https://openalex.org/W2120370440","https://openalex.org/W2131735685","https://openalex.org/W2145017601","https://openalex.org/W2158112438","https://openalex.org/W2167395549","https://openalex.org/W2269718938","https://openalex.org/W2291960678","https://openalex.org/W2342772136","https://openalex.org/W2477921776","https://openalex.org/W2488775294","https://openalex.org/W2489930379","https://openalex.org/W2732661672","https://openalex.org/W2990946391","https://openalex.org/W3022585649","https://openalex.org/W4212798850","https://openalex.org/W4236165936","https://openalex.org/W4244684117","https://openalex.org/W4247877478","https://openalex.org/W4248933783","https://openalex.org/W4253399077","https://openalex.org/W4256340197","https://openalex.org/W4388391905","https://openalex.org/W6634467100","https://openalex.org/W6683593063"],"related_works":["https://openalex.org/W1994822208","https://openalex.org/W2124138615","https://openalex.org/W1981721685","https://openalex.org/W2068505497","https://openalex.org/W4366196986","https://openalex.org/W2370498728","https://openalex.org/W2072834359","https://openalex.org/W2383506381","https://openalex.org/W4242356838","https://openalex.org/W2141533127"],"abstract_inverted_index":{"Two":[0],"approaches":[1],"resulting":[2],"in":[3,34],"two":[4],"different":[5],"generalizations":[6],"of":[7,37],"the":[8,28,35,44,52,58],"space-time-fractional":[9],"advection-diffusion":[10],"equation":[11],"are":[12,22,41,64],"discussed.":[13],"The":[14,24,61],"Caputo":[15],"time-fractional":[16],"derivative":[17],"and":[18,31,51],"Riesz":[19],"fractional":[20],"Laplacian":[21],"used.":[23],"fundamental":[25],"solutions":[26],"to":[27,49,57],"corresponding":[29],"Cauchy":[30],"source":[32],"problems":[33],"case":[36],"one":[38],"spatial":[39,59],"variable":[40],"studied":[42],"using":[43],"Laplace":[45],"transform":[46,54],"with":[47,55],"respect":[48,56],"time":[50],"Fourier":[53],"coordinate.":[60],"numerical":[62],"results":[63],"illustrated":[65],"graphically.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
