{"id":"https://openalex.org/W2092884876","doi":"https://doi.org/10.1137/090775920","title":"Fractional Cable Equation Models for Anomalous Electrodiffusion in Nerve Cells: Finite Domain Solutions","display_name":"Fractional Cable Equation Models for Anomalous Electrodiffusion in Nerve Cells: Finite Domain Solutions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2092884876","doi":"https://doi.org/10.1137/090775920","mag":"2092884876"},"language":"en","primary_location":{"id":"doi:10.1137/090775920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775920","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied 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/A5080301011","display_name":"T. A. M. Langlands","orcid":"https://orcid.org/0000-0001-7679-6891"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"T. A. M. Langlands","raw_affiliation_strings":["Department of Applied Mathematics, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076033510","display_name":"B. I. Henry","orcid":"https://orcid.org/0000-0002-4387-6155"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"B. I. Henry","raw_affiliation_strings":["Department of Applied Mathematics, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061940577","display_name":"Susan L. Wearne","orcid":null},"institutions":[{"id":"https://openalex.org/I98704320","display_name":"Icahn School of Medicine at Mount Sinai","ror":"https://ror.org/04a9tmd77","country_code":"US","type":"education","lineage":["https://openalex.org/I1320796813","https://openalex.org/I98704320"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. L. Wearne","raw_affiliation_strings":["Laboratory for Biomathematical Sciences, Department of Neuroscience, Mount Sinai School of Medicine, New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Biomathematical Sciences, Department of Neuroscience, Mount Sinai School of Medicine, New York, USA","institution_ids":["https://openalex.org/I98704320"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8274,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.90894668,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"71","issue":"4","first_page":"1168","last_page":"1203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9980999827384949,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9972000122070312,"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/T10493","display_name":"Ion channel regulation and function","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cable-theory","display_name":"Cable theory","score":0.7500667572021484},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6471978425979614},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.6240577101707458},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.5882949233055115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.547374963760376},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4944336414337158},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4633190333843231},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.45293691754341125},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4328407347202301},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4116297662258148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2766275405883789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10560441017150879},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10102382302284241},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07985463738441467}],"concepts":[{"id":"https://openalex.org/C59399137","wikidata":"https://www.wikidata.org/wiki/Q1327423","display_name":"Cable theory","level":4,"score":0.7500667572021484},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6471978425979614},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.6240577101707458},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.5882949233055115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.547374963760376},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4944336414337158},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4633190333843231},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.45293691754341125},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4328407347202301},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4116297662258148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2766275405883789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10560441017150879},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10102382302284241},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07985463738441467},{"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},{"id":"https://openalex.org/C180761244","wikidata":"https://www.wikidata.org/wiki/Q354262","display_name":"Cable harness","level":3,"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/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C110925319","wikidata":"https://www.wikidata.org/wiki/Q12855","display_name":"Cable gland","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090775920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775920","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.usq.edu.au:20048","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400692","display_name":"University of Southern Queensland ePrints (University of Southern Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I185523456","host_organization_name":"University of Southern Queensland","host_organization_lineage":["https://openalex.org/I185523456"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article (Commonwealth Reporting Category C)"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W60166153","https://openalex.org/W122352469","https://openalex.org/W236966125","https://openalex.org/W1512746852","https://openalex.org/W1517714302","https://openalex.org/W1559873805","https://openalex.org/W1566861944","https://openalex.org/W1600950487","https://openalex.org/W1601216305","https://openalex.org/W1964684947","https://openalex.org/W1967200406","https://openalex.org/W1967305191","https://openalex.org/W1969584830","https://openalex.org/W1976130185","https://openalex.org/W1976658425","https://openalex.org/W1976776824","https://openalex.org/W1980290602","https://openalex.org/W1987317750","https://openalex.org/W1989307095","https://openalex.org/W1989941945","https://openalex.org/W1996196738","https://openalex.org/W1997105777","https://openalex.org/W1998399256","https://openalex.org/W2000817298","https://openalex.org/W2002478108","https://openalex.org/W2006991582","https://openalex.org/W2013812365","https://openalex.org/W2028252724","https://openalex.org/W2029483703","https://openalex.org/W2034352409","https://openalex.org/W2037013349","https://openalex.org/W2040194422","https://openalex.org/W2043880524","https://openalex.org/W2046320783","https://openalex.org/W2047857096","https://openalex.org/W2049662054","https://openalex.org/W2052671664","https://openalex.org/W2055862760","https://openalex.org/W2060650941","https://openalex.org/W2062089923","https://openalex.org/W2072073939","https://openalex.org/W2072638029","https://openalex.org/W2077511050","https://openalex.org/W2077807867","https://openalex.org/W2080661489","https://openalex.org/W2081118982","https://openalex.org/W2091256898","https://openalex.org/W2091442483","https://openalex.org/W2097711273","https://openalex.org/W2105713043","https://openalex.org/W2110427436","https://openalex.org/W2111072798","https://openalex.org/W2111271983","https://openalex.org/W2125366357","https://openalex.org/W2134219317","https://openalex.org/W2144858695","https://openalex.org/W2151015649","https://openalex.org/W2155252492","https://openalex.org/W2156353832","https://openalex.org/W2156458781","https://openalex.org/W2156961733","https://openalex.org/W2158972649","https://openalex.org/W2169530852","https://openalex.org/W2170159961","https://openalex.org/W2787959293","https://openalex.org/W3100162194","https://openalex.org/W3102939200"],"related_works":["https://openalex.org/W2243040821","https://openalex.org/W4250916133","https://openalex.org/W2619027208","https://openalex.org/W4287755247","https://openalex.org/W2043273258","https://openalex.org/W1568591221","https://openalex.org/W2004351213","https://openalex.org/W2142523768","https://openalex.org/W4376879885","https://openalex.org/W109261043"],"abstract_inverted_index":{"In":[0],"recent":[1,56],"work":[2,31],"we":[3,100],"introduced":[4],"fractional":[5,10,87,144],"Nernst\u2013Planck":[6],"equations":[7,12,89],"and":[8,25,37,90,96,151],"related":[9],"cable":[11,88,145],"to":[13,72,85,190],"model":[14,115],"electrodiffusion":[15],"of":[16,119,135],"ions":[17],"in":[18,46,68,81],"nerve":[19,28,154],"cells":[20],"with":[21,49,124,220],"anomalous":[22,42,61,171,178,201],"subdiffusion":[23,62,80,149,175,198],"along":[24,64,150,179,202],"across":[26,152],"the":[27,65,75,79,136,153,156,159,165,170,174,180,187,197,203,207],"cells.":[29],"This":[30],"was":[32],"motivated":[33],"by":[34,74,169],"many":[35],"computational":[36],"experimental":[38],"studies":[39],"showing":[40],"that":[41,60,126],"diffusion":[43],"is":[44,140,167,176,199],"ubiquitous":[45],"biological":[47],"systems":[48],"binding,":[50],"crowding,":[51],"or":[52,131],"trapping.":[53],"For":[54],"example,":[55],"experiments":[57,223],"have":[58],"shown":[59],"occurs":[63],"axial":[66,181,204],"direction":[67],"spiny":[69,120],"dendrites":[70],"due":[71],"trapping":[73],"spines.":[76],"We":[77],"modeled":[78],"two":[82,86],"ways":[83],"leading":[84],"presented":[91],"fundamental":[92],"solutions":[93,102,114,139,216],"on":[94,103,224],"infinite":[95],"semi-infinite":[97],"domains.":[98],"Here":[99],"present":[101],"finite":[104,112,137],"domains":[105],"for":[106,142],"mixed":[107],"Robin":[108],"boundary":[109],"conditions.":[110],"The":[111,133],"domain":[113,138],"passive":[116],"electrotonic":[117],"properties":[118],"dendritic":[121],"branch":[122],"segments":[123],"ends":[125],"are":[127],"voltage":[128],"clamped,":[129],"sealed,":[130],"killed.":[132],"behavior":[134],"similar":[141],"both":[143],"equations.":[146],"With":[147],"uniform":[148],"cells,":[155],"solution":[157,188,208],"approaches":[158,209],"standard":[160],"nonzero":[161],"steady":[162,193,213],"state,":[163,194],"but":[164],"approach":[166],"slowed":[168],"subdiffusion.":[172],"If":[173],"more":[177],"direction,":[182,205],"then":[183,206],"(boundary":[184],"conditions":[185],"permitting)":[186],"converges":[189],"a":[191,210],"zero":[192],"whereas":[195],"if":[196],"less":[200],"spatially":[211],"linear":[212],"state.":[214],"These":[215],"could":[217],"be":[218],"compared":[219],"realistic":[221],"electrophysiological":[222],"actual":[225],"dendrites.":[226]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}