{"id":"https://openalex.org/W1983398677","doi":"https://doi.org/10.2478/s13540-011-0005-9","title":"Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations","display_name":"Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations","publication_year":2011,"publication_date":"2011-01-14","ids":{"openalex":"https://openalex.org/W1983398677","doi":"https://doi.org/10.2478/s13540-011-0005-9","mag":"1983398677"},"language":"en","primary_location":{"id":"doi:10.2478/s13540-011-0005-9","doi":"https://doi.org/10.2478/s13540-011-0005-9","is_oa":false,"landing_page_url":"https://doi.org/10.2478/s13540-011-0005-9","pdf_url":null,"source":{"id":"https://openalex.org/S113036218","display_name":"Fractional Calculus and Applied Analysis","issn_l":"1311-0454","issn":["1311-0454","1314-2224"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractional Calculus and Applied Analysis","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10525/1682","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062442470","display_name":"Marjorie G. Hahn","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marjorie Hahn","raw_affiliation_strings":["Department of Mathematics, Tufts University, Medford, MA, 02155, USA","Tufts University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tufts University, Medford, MA, 02155, USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Tufts University","institution_ids":["https://openalex.org/I121934306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062805599","display_name":"Sabir R. Umarov","orcid":"https://orcid.org/0000-0002-9912-7233","observed_orcids":["https://orcid.org/0000-0002-9912-7233"]},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sabir Umarov","raw_affiliation_strings":["Department of Mathematics, Tufts University, Medford, MA, 02155, USA","Tufts University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tufts University, Medford, MA, 02155, USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Tufts University","institution_ids":["https://openalex.org/I121934306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062442470"],"corresponding_institution_ids":["https://openalex.org/I121934306"],"apc_list":{"value":2590,"currency":"USD","value_usd":2590},"apc_paid":null,"fwci":3.8458,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.91736896,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"14","issue":"1","first_page":"56","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9580000042915344,"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":0.9580000042915344,"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":0.011099999770522118,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.008500000461935997,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/stochastic-differential-equations","display_name":"stochastic differential equations","score":0.8349999785423279},{"id":"https://openalex.org/keywords/ito-calculus","display_name":"It\u00f4 calculus","score":0.6949999928474426},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"fractional calculus","score":0.6520000100135803},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.7459999918937683},{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"fractional Brownian motion","score":0.6140000224113464},{"id":"https://openalex.org/keywords/partial-differential-equations","display_name":"partial differential equations","score":0.5070000290870667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8043233752250671},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.7688740491867065},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7162333130836487},{"id":"https://openalex.org/C59465623","wikidata":"https://www.wikidata.org/wiki/Q6427428","display_name":"Kolmogorov equations (Markov jump process)","level":5,"score":0.6876793503761292},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.5788543820381165},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.5690043568611145},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5345085859298706},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.49141037464141846},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4613184630870819},{"id":"https://openalex.org/C101615488","wikidata":"https://www.wikidata.org/wiki/Q1503307","display_name":"Geometric Brownian motion","level":4,"score":0.4116099178791046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40696004033088684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.366934597492218},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.3578929305076599},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.1312463879585266},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.12565341591835022},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05993169546127319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05843999981880188},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/s13540-011-0005-9","doi":"https://doi.org/10.2478/s13540-011-0005-9","is_oa":false,"landing_page_url":"https://doi.org/10.2478/s13540-011-0005-9","pdf_url":null,"source":{"id":"https://openalex.org/S113036218","display_name":"Fractional Calculus and Applied Analysis","issn_l":"1311-0454","issn":["1311-0454","1314-2224"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractional Calculus and Applied Analysis","raw_type":"journal-article"},{"id":"pmh:oai:bpos.bg:2122","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10525/1682","pdf_url":null,"source":{"id":"https://openalex.org/S7407055231","display_name":"Bulgarian Portal for Open Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"other"},{"id":"pmh:oai:sci-gems.math.bas.bg:10525/1682","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10525/1682","pdf_url":null,"source":{"id":"https://openalex.org/S4306401343","display_name":"Bulgarian Digital Mathematics Library (BulDML) at IMI-BAS (Institute of Mathematics and Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210105926","host_organization_name":"Institute of Mathematics and Informatics","host_organization_lineage":["https://openalex.org/I4210105926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:bpos.bg:2122","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10525/1682","pdf_url":null,"source":{"id":"https://openalex.org/S7407055231","display_name":"Bulgarian Portal for Open Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"other"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W162050314","https://openalex.org/W579048987","https://openalex.org/W607600043","https://openalex.org/W1214703565","https://openalex.org/W1489022300","https://openalex.org/W1495987901","https://openalex.org/W1504271241","https://openalex.org/W1528987510","https://openalex.org/W1544159280","https://openalex.org/W1565709553","https://openalex.org/W1584138300","https://openalex.org/W1591798773","https://openalex.org/W1614690037","https://openalex.org/W1667003406","https://openalex.org/W1870957188","https://openalex.org/W1974234252","https://openalex.org/W1974258811","https://openalex.org/W1977360274","https://openalex.org/W1980147450","https://openalex.org/W1989941945","https://openalex.org/W1990932185","https://openalex.org/W1995522593","https://openalex.org/W1997050292","https://openalex.org/W2039324033","https://openalex.org/W2044729651","https://openalex.org/W2049503097","https://openalex.org/W2053248030","https://openalex.org/W2064361774","https://openalex.org/W2068724733","https://openalex.org/W2076413989","https://openalex.org/W2081877251","https://openalex.org/W2083488564","https://openalex.org/W2094830203","https://openalex.org/W2099111135","https://openalex.org/W2105451800","https://openalex.org/W2106786121","https://openalex.org/W2108823069","https://openalex.org/W2111271983","https://openalex.org/W2129007952","https://openalex.org/W2147688960","https://openalex.org/W2151667150","https://openalex.org/W2158112438","https://openalex.org/W2159596543","https://openalex.org/W2482327740","https://openalex.org/W2490827572","https://openalex.org/W2502482606","https://openalex.org/W2797641211","https://openalex.org/W2799137445","https://openalex.org/W2802739963","https://openalex.org/W2954974458","https://openalex.org/W2962818245","https://openalex.org/W2962874481","https://openalex.org/W2963589517","https://openalex.org/W3098224580","https://openalex.org/W3103744012","https://openalex.org/W3212699936","https://openalex.org/W4247371619","https://openalex.org/W4297584681","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W3129602449","https://openalex.org/W2384879887","https://openalex.org/W2375736556","https://openalex.org/W2142979439","https://openalex.org/W2380610144","https://openalex.org/W2786290219","https://openalex.org/W2963836928","https://openalex.org/W4382939522","https://openalex.org/W2179633876","https://openalex.org/W4319791984"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}