{"id":"https://openalex.org/W1616749415","doi":"https://doi.org/10.1109/mmar.2015.7283893","title":"2D space-time fractional diffusion on bounded domain — Application of the fractional Sturm-Liouville theory","display_name":"2D space-time fractional diffusion on bounded domain — Application of the fractional Sturm-Liouville theory","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W1616749415","doi":"https://doi.org/10.1109/mmar.2015.7283893","mag":"1616749415"},"language":"en","primary_location":{"id":"doi:10.1109/mmar.2015.7283893","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2015.7283893","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR)","raw_type":"proceedings-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/A5001274870","display_name":"Ma\u0142gorzata Klimek","orcid":"https://orcid.org/0000-0002-1029-1863"},"institutions":[{"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"]},{"id":"https://openalex.org/I130294970","display_name":"Cz\u0119stochowa University of Technology","ror":"https://ror.org/046awyn59","country_code":"PL","type":"education","lineage":["https://openalex.org/I130294970"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Malgorzata Klimek","raw_affiliation_strings":["Institute of Mathematics, Czestochowa University of Technology, Czestochowa, Poland","Institute of Mathematics, Cz\u0119stochowa University of Technology, Cz\u0119stochowa, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Czestochowa University of Technology, Czestochowa, Poland","institution_ids":["https://openalex.org/I130294970","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics, Cz\u0119stochowa University of Technology, Cz\u0119stochowa, Poland","institution_ids":["https://openalex.org/I130294970","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001274870"],"corresponding_institution_ids":["https://openalex.org/I130294970","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02670251,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"74","issue":null,"first_page":"309","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/bounded-function","display_name":"Bounded function","score":0.8105148077011108},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.7876603603363037},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7669945359230042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6801636815071106},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6144859194755554},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5581759810447693},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5379242897033691},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5120437741279602},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5088560581207275},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4924953877925873},{"id":"https://openalex.org/keywords/riesz-potential","display_name":"Riesz potential","score":0.44503673911094666},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.43569377064704895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17572033405303955},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13547727465629578},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12710168957710266},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08565017580986023}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8105148077011108},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7876603603363037},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7669945359230042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6801636815071106},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6144859194755554},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5581759810447693},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5379242897033691},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5120437741279602},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5088560581207275},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4924953877925873},{"id":"https://openalex.org/C189987565","wikidata":"https://www.wikidata.org/wiki/Q7333166","display_name":"Riesz potential","level":2,"score":0.44503673911094666},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.43569377064704895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17572033405303955},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13547727465629578},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12710168957710266},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08565017580986023},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/mmar.2015.7283893","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2015.7283893","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W260145074","https://openalex.org/W958238625","https://openalex.org/W1584611818","https://openalex.org/W1971200514","https://openalex.org/W1975765037","https://openalex.org/W1987117770","https://openalex.org/W1992614405","https://openalex.org/W2060825796","https://openalex.org/W2061262082","https://openalex.org/W2067313050","https://openalex.org/W2072995473","https://openalex.org/W2075267567","https://openalex.org/W2082817084","https://openalex.org/W2085402108","https://openalex.org/W2118288723","https://openalex.org/W2132997731","https://openalex.org/W2133253521","https://openalex.org/W2162592888","https://openalex.org/W2171679020","https://openalex.org/W2278774777","https://openalex.org/W2308190093","https://openalex.org/W2741359054","https://openalex.org/W2787959293","https://openalex.org/W2962785683","https://openalex.org/W6741721475"],"related_works":["https://openalex.org/W2061779639","https://openalex.org/W2006059763","https://openalex.org/W4361278152","https://openalex.org/W2081617345","https://openalex.org/W4287727929","https://openalex.org/W3038146150","https://openalex.org/W2162375460","https://openalex.org/W2357178983","https://openalex.org/W2061111199","https://openalex.org/W2930126963"],"abstract_inverted_index":{"In":[0,46,63],"the":[1,20,28,47,53,59,64,70,76],"paper,":[2],"we":[3,49,67],"construct":[4],"a":[5,9,16,37],"weak":[6],"solution":[7,74],"to":[8,58,75],"2D":[10],"space-time":[11],"fractional":[12,21,54],"diffusion":[13],"problem":[14,56],"in":[15,27],"bounded":[17],"domain,":[18],"provided":[19],"orders":[22],"of":[23,40,52],"Riesz":[24,41],"derivatives":[25,42],"are":[26],"range":[29],"(1,":[30],"2).":[31],"The":[32],"spatial":[33],"differential":[34],"operator":[35],"includes":[36],"non-symmetric":[38],"combination":[39],"and":[43],"variable":[44],"diffusivities.":[45],"construction,":[48],"apply":[50],"eigenfunctions":[51],"Sturm-Liouville":[55],"subjected":[57],"mixed":[60],"boundary":[61],"conditions.":[62],"main":[65],"theorem":[66],"describe":[68],"explicitly":[69],"unique,":[71],"real-valued":[72],"continuous":[73],"problem.":[77]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}