{"id":"https://openalex.org/W2000526322","doi":"https://doi.org/10.1016/s0301-0104(02)00537-2","title":"Space- and time-fractional diffusion and wave equations, fractional Fokker\u2013Planck equations, and physical motivation","display_name":"Space- and time-fractional diffusion and wave equations, fractional Fokker\u2013Planck equations, and physical motivation","publication_year":2002,"publication_date":"2002-10-21","ids":{"openalex":"https://openalex.org/W2000526322","doi":"https://doi.org/10.1016/s0301-0104(02)00537-2","mag":"2000526322"},"language":"en","primary_location":{"id":"doi:10.1016/s0301-0104(02)00537-2","doi":"https://doi.org/10.1016/s0301-0104(02)00537-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0301-0104(02)00537-2","pdf_url":null,"source":{"id":"https://openalex.org/S190037396","display_name":"Chemical Physics","issn_l":"0301-0104","issn":["0301-0104","1873-4421"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chemical Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5044662930","display_name":"Ralf Metzler","orcid":"https://orcid.org/0000-0002-6013-7020","observed_orcids":["https://orcid.org/0000-0002-6013-7020"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ralf Metzler","raw_affiliation_strings":["Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","NORDITA, Blegdamsvej 17, DK-2100 K\u00f8benhavn \u00d8, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"NORDITA, Blegdamsvej 17, DK-2100 K\u00f8benhavn \u00d8, Denmark","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113571848","display_name":"Theo F. Nonnenmacher","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Theo F. Nonnenmacher","raw_affiliation_strings":["Department of Mathematical Physics, University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm/Donau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Physics, University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm/Donau, Germany","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044662930"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":{"value":3690,"currency":"USD","value_usd":3690},"apc_paid":null,"fwci":10.4392,"has_fulltext":false,"cited_by_count":218,"citation_normalized_percentile":{"value":0.97720798,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"284","issue":"1-2","first_page":"67","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.899399995803833,"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":0.899399995803833,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.09910000115633011,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/space-fractional-diffusion-equation","display_name":"space-fractional diffusion equation","score":0.9190000295639038},{"id":"https://openalex.org/keywords/time-fractional-diffusion-equation","display_name":"time-fractional diffusion equation","score":0.9900000095367432},{"id":"https://openalex.org/keywords/fractional-wave-equation","display_name":"fractional wave equation","score":0.9210000038146973},{"id":"https://openalex.org/keywords/fractional-fokker-planck-equation","display_name":"fractional Fokker-Planck equation","score":0.9810000061988831},{"id":"https://openalex.org/keywords/levy-flight","display_name":"L\u00e9vy flight","score":0.7940000295639038},{"id":"https://openalex.org/keywords/long-waiting-times","display_name":"long waiting times","score":0.8539999723434448},{"id":"https://openalex.org/keywords/random-walkers","display_name":"random walkers","score":0.6330000162124634},{"id":"https://openalex.org/keywords/fractional-kinetic-equations","display_name":"fractional kinetic equations","score":0.8270000219345093},{"id":"https://openalex.org/keywords/nonequilibrium-relaxation","display_name":"nonequilibrium relaxation","score":0.8190000057220459},{"id":"https://openalex.org/keywords/explicit-solutions","display_name":"explicit solutions","score":0.9079999923706055}],"concepts":[{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.8083090782165527},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.646988570690155},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5847105383872986},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5101342797279358},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5090146064758301},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4623623490333557},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.42085781693458557},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.39048516750335693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3141736090183258},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3052014410495758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26925337314605713},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.18857380747795105},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12826290726661682},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0301-0104(02)00537-2","doi":"https://doi.org/10.1016/s0301-0104(02)00537-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0301-0104(02)00537-2","pdf_url":null,"source":{"id":"https://openalex.org/S190037396","display_name":"Chemical Physics","issn_l":"0301-0104","issn":["0301-0104","1873-4421"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Chemical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":124,"referenced_works":["https://openalex.org/W122352469","https://openalex.org/W145038029","https://openalex.org/W568542710","https://openalex.org/W584754793","https://openalex.org/W940516314","https://openalex.org/W1519208961","https://openalex.org/W1557758852","https://openalex.org/W1559873805","https://openalex.org/W1591581817","https://openalex.org/W1622275976","https://openalex.org/W1703275993","https://openalex.org/W1816275442","https://openalex.org/W1873431535","https://openalex.org/W1895946677","https://openalex.org/W1964684947","https://openalex.org/W1966793822","https://openalex.org/W1967200406","https://openalex.org/W1968481081","https://openalex.org/W1968823430","https://openalex.org/W1972142370","https://openalex.org/W1973950856","https://openalex.org/W1974782455","https://openalex.org/W1974824584","https://openalex.org/W1976962685","https://openalex.org/W1977431865","https://openalex.org/W1978411449","https://openalex.org/W1986257969","https://openalex.org/W1987284211","https://openalex.org/W1987288036","https://openalex.org/W1992295222","https://openalex.org/W1992659238","https://openalex.org/W1992787938","https://openalex.org/W1993774330","https://openalex.org/W1995301856","https://openalex.org/W2001041648","https://openalex.org/W2004097100","https://openalex.org/W2005300419","https://openalex.org/W2005308357","https://openalex.org/W2009387827","https://openalex.org/W2009714004","https://openalex.org/W2010264617","https://openalex.org/W2011641151","https://openalex.org/W2012021517","https://openalex.org/W2012029574","https://openalex.org/W2013104836","https://openalex.org/W2013319626","https://openalex.org/W2013348880","https://openalex.org/W2016437223","https://openalex.org/W2018674686","https://openalex.org/W2018965660","https://openalex.org/W2019194978","https://openalex.org/W2024213285","https://openalex.org/W2027076061","https://openalex.org/W2030733650","https://openalex.org/W2030765885","https://openalex.org/W2033102362","https://openalex.org/W2036007974","https://openalex.org/W2036969848","https://openalex.org/W2037028678","https://openalex.org/W2037200286","https://openalex.org/W2038936757","https://openalex.org/W2039213653","https://openalex.org/W2039497549","https://openalex.org/W2040194422","https://openalex.org/W2040675064","https://openalex.org/W2044519862","https://openalex.org/W2045514685","https://openalex.org/W2046613707","https://openalex.org/W2046712495","https://openalex.org/W2048184127","https://openalex.org/W2050492371","https://openalex.org/W2050776089","https://openalex.org/W2053324351","https://openalex.org/W2053363673","https://openalex.org/W2054912878","https://openalex.org/W2055922934","https://openalex.org/W2056820162","https://openalex.org/W2058244770","https://openalex.org/W2062087171","https://openalex.org/W2062517214","https://openalex.org/W2063404874","https://openalex.org/W2063886361","https://openalex.org/W2066797413","https://openalex.org/W2071034248","https://openalex.org/W2075071269","https://openalex.org/W2078420365","https://openalex.org/W2078833414","https://openalex.org/W2080433292","https://openalex.org/W2081925484","https://openalex.org/W2083564782","https://openalex.org/W2084058002","https://openalex.org/W2084163579","https://openalex.org/W2084686033","https://openalex.org/W2085266415","https://openalex.org/W2085440349","https://openalex.org/W2087632023","https://openalex.org/W2087935134","https://openalex.org/W2091737770","https://openalex.org/W2093067381","https://openalex.org/W2093744628","https://openalex.org/W2098793851","https://openalex.org/W2102787760","https://openalex.org/W2111271983","https://openalex.org/W2112360585","https://openalex.org/W2113687945","https://openalex.org/W2114849571","https://openalex.org/W2136872267","https://openalex.org/W2156649359","https://openalex.org/W2162488624","https://openalex.org/W2167384544","https://openalex.org/W2323297864","https://openalex.org/W2323857126","https://openalex.org/W2334415579","https://openalex.org/W2518715101","https://openalex.org/W2611011638","https://openalex.org/W2611283763","https://openalex.org/W2754418952","https://openalex.org/W2942588749","https://openalex.org/W2996644363","https://openalex.org/W4240384253","https://openalex.org/W4245911052","https://openalex.org/W4249653603","https://openalex.org/W4255141406","https://openalex.org/W4298071626"],"related_works":["https://openalex.org/W2040194422","https://openalex.org/W6959650823","https://openalex.org/W7027465169","https://openalex.org/W2055421059","https://openalex.org/W2009714004","https://openalex.org/W2013812365","https://openalex.org/W2062040958","https://openalex.org/W2946091255","https://openalex.org/W4382808493","https://openalex.org/W2111271983"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
