{"id":"https://openalex.org/W2782391857","doi":"https://doi.org/10.1080/00207160.2017.1421949","title":"Fractional pseudo-spectral methods for distributed-order fractional PDEs","display_name":"Fractional pseudo-spectral methods for distributed-order fractional PDEs","publication_year":2018,"publication_date":"2018-01-04","ids":{"openalex":"https://openalex.org/W2782391857","doi":"https://doi.org/10.1080/00207160.2017.1421949","mag":"2782391857"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1421949","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1421949","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-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/A5026301782","display_name":"Ehsan Kharazmi","orcid":"https://orcid.org/0000-0002-3680-5500"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ehsan Kharazmi","raw_affiliation_strings":["Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA","Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051268633","display_name":"Mohsen Zayernouri","orcid":"https://orcid.org/0000-0002-0831-2610"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mohsen Zayernouri","raw_affiliation_strings":["Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA","Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051268633"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":4.2578,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.94653154,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"95","issue":"6-7","first_page":"1340","last_page":"1361"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9969000220298767,"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":0.8351471424102783},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5860479474067688},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5850043892860413},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5378102660179138},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49586614966392517},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4927423298358917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4753391742706299},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4503291845321655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4300426244735718},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.41922321915626526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10013920068740845},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.09494549036026001}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8351471424102783},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5860479474067688},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5850043892860413},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5378102660179138},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49586614966392517},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4927423298358917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4753391742706299},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4503291845321655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4300426244735718},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.41922321915626526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10013920068740845},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.09494549036026001},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1421949","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1421949","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4420234770","display_name":null,"funder_award_id":"FA9550-17-1-0150","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W104068007","https://openalex.org/W110340196","https://openalex.org/W620183161","https://openalex.org/W755756226","https://openalex.org/W1131718341","https://openalex.org/W1531510807","https://openalex.org/W1553338987","https://openalex.org/W1966513244","https://openalex.org/W1967569646","https://openalex.org/W1969312973","https://openalex.org/W1975900429","https://openalex.org/W1980479723","https://openalex.org/W1981384091","https://openalex.org/W1983159263","https://openalex.org/W1986915637","https://openalex.org/W1987452198","https://openalex.org/W1987597560","https://openalex.org/W1993445800","https://openalex.org/W2004467399","https://openalex.org/W2006907269","https://openalex.org/W2009456713","https://openalex.org/W2014254762","https://openalex.org/W2019659177","https://openalex.org/W2025672056","https://openalex.org/W2026946703","https://openalex.org/W2029878293","https://openalex.org/W2030146312","https://openalex.org/W2035830378","https://openalex.org/W2052623210","https://openalex.org/W2053256951","https://openalex.org/W2057127233","https://openalex.org/W2063589755","https://openalex.org/W2065254635","https://openalex.org/W2090239694","https://openalex.org/W2091740033","https://openalex.org/W2095472505","https://openalex.org/W2098803915","https://openalex.org/W2104055838","https://openalex.org/W2110245394","https://openalex.org/W2114010261","https://openalex.org/W2136196792","https://openalex.org/W2137120557","https://openalex.org/W2137696066","https://openalex.org/W2145803046","https://openalex.org/W2148320567","https://openalex.org/W2161513111","https://openalex.org/W2165076033","https://openalex.org/W2251960872","https://openalex.org/W2268987813","https://openalex.org/W2410657832","https://openalex.org/W2512232321","https://openalex.org/W2541035753","https://openalex.org/W2605056791","https://openalex.org/W2618423736","https://openalex.org/W2765447624","https://openalex.org/W2787959293","https://openalex.org/W2963805080"],"related_works":["https://openalex.org/W4311624594","https://openalex.org/W1968147478","https://openalex.org/W2090149457","https://openalex.org/W2134815061","https://openalex.org/W1979931392","https://openalex.org/W1999570265","https://openalex.org/W3184839022","https://openalex.org/W2750561019","https://openalex.org/W2319417348","https://openalex.org/W2089028757"],"abstract_inverted_index":{"We":[0,21,55],"develop":[1],"a":[2],"pseudo-spectral":[3],"method":[4],"of":[5,15,42,75,85,105],"Petrov\u2013Galerkin":[6],"sense,":[7],"employing":[8],"nodal":[9,49],"expansions":[10],"in":[11],"the":[12,23,29,35,38,48,57,64,76,83,92,106],"weak":[13,59],"formulation":[14],"distributed-order":[16,121,128],"fractional":[17,39,68],"partial":[18],"differential":[19],"equations.":[20],"define":[22],"underlying":[24],"distributed":[25,60,99],"Sobolev":[26],"spaces":[27],"and":[28,44,51,88,95,124],"associated":[30],"norms.":[31],"Then,":[32],"we":[33,81,102],"formulate":[34],"scheme,":[36],"using":[37],"Lagrange":[40],"interpolants":[41],"first":[43],"second":[45],"kind":[46],"as":[47],"bases":[50],"test":[52],"functions,":[53],"respectively.":[54],"construct":[56],"corresponding":[58],"differentiation":[61],"matrices":[62],"for":[63],"operators":[65],"with":[66],"one-/two-sided":[67],"derivatives,":[69],"leading":[70],"to":[71],"an":[72],"improved":[73],"conditioning":[74],"resulting":[77],"linear":[78],"system.":[79],"Subsequently,":[80],"study":[82],"effect":[84],"distribution":[86],"function":[87],"interpolation":[89],"points":[90],"on":[91],"condition":[93],"number,":[94],"further":[96],"design":[97],"several":[98,111],"pre-conditioners.":[100],"Furthermore,":[101],"investigate":[103],"efficiency":[104],"proposed":[107],"scheme":[108],"by":[109],"considering":[110],"linear/nonlinear":[112],"numerical":[113],"examples,":[114],"including":[115],"initial":[116],"value":[117],"problem,":[118],"(1+1)-D":[119],"space":[120,127],"Burgers'":[122],"equation,":[123],"(1+2)-D":[125],"two-sided":[126],"nonlinear":[129],"reaction\u2013diffusion":[130],"equation.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}
