{"id":"https://openalex.org/W4362586794","doi":"https://doi.org/10.1007/s40314-023-02274-1","title":"Constructing reliable approximations of the random fractional Hermite equation: solution, moments and density","display_name":"Constructing reliable approximations of the random fractional Hermite equation: solution, moments and density","publication_year":2023,"publication_date":"2023-04-01","ids":{"openalex":"https://openalex.org/W4362586794","doi":"https://doi.org/10.1007/s40314-023-02274-1"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-023-02274-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-023-02274-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-023-02274-1.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-023-02274-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045706308","display_name":"C. Burgos","orcid":"https://orcid.org/0000-0001-6385-4263"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Clara Burgos","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain"],"raw_orcid":"https://orcid.org/0000-0001-6385-4263","affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085582592","display_name":"Tom\u00e1s Caraballo","orcid":"https://orcid.org/0000-0003-4697-898X"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Tom\u00e1s Caraballo","raw_affiliation_strings":["Departamento de ecuaciones diferenciales y an\u00e1lislsl num\u00e9rico, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012, Seville, Spain","Departamento de ecuaciones diferenciales y an\u00e1lislsl num\u00e9rico, Universidad de Sevilla, Seville, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de ecuaciones diferenciales y an\u00e1lislsl num\u00e9rico, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Departamento de ecuaciones diferenciales y an\u00e1lislsl num\u00e9rico, Universidad de Sevilla, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001284929","display_name":"J.\u2010C. Cort\u00e9s","orcid":"https://orcid.org/0000-0002-6528-2155"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan Carlos Cort\u00e9s","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009864461","display_name":"L. Villafuerte","orcid":"https://orcid.org/0000-0001-8281-2819"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Laura Villafuerte","raw_affiliation_strings":["Department of Mathematics, University of Texas at Austin USA, Austin, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Austin USA, Austin, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081099253","display_name":"Rafael J. Villanueva","orcid":"https://orcid.org/0000-0002-0131-0532"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael Jacinto Villanueva","raw_affiliation_strings":["Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de vera s/n, 46022, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"Instituto Universitario de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5045706308"],"corresponding_institution_ids":["https://openalex.org/I60053951"],"apc_list":null,"apc_paid":null,"fwci":0.2098,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45005637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"42","issue":"3","first_page":null,"last_page":null},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9869999885559082,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9857000112533569,"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/mathematics","display_name":"Mathematics","score":0.8137409090995789},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.7481499910354614},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5630699396133423},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4914356470108032},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.47546929121017456},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.46129974722862244},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.43996328115463257},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4188833236694336},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3732520639896393},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10983285307884216}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8137409090995789},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7481499910354614},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5630699396133423},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4914356470108032},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.47546929121017456},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.46129974722862244},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.43996328115463257},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4188833236694336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3732520639896393},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10983285307884216},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s40314-023-02274-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-023-02274-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-023-02274-1.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:riunet.upv.es:10251/205811","is_oa":true,"landing_page_url":"http://hdl.handle.net/10251/205811","pdf_url":null,"source":{"id":"https://openalex.org/S4306401500","display_name":"RiuNet (Politechnical University of Valencia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60053951","host_organization_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","host_organization_lineage":["https://openalex.org/I60053951"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s40314-023-02274-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-023-02274-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-023-02274-1.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1422035950","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"},{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1714292816","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2713276326","display_name":null,"funder_award_id":"by MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G320108333","display_name":null,"funder_award_id":"AICO/2021/302","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"},{"id":"https://openalex.org/G3219925899","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4444445591","display_name":null,"funder_award_id":"PID2020-115270GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320321864","display_name":"Generalitat Valenciana","ror":"https://ror.org/0097mvx21"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4362586794.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W41192749","https://openalex.org/W1496857014","https://openalex.org/W1976487420","https://openalex.org/W1997357077","https://openalex.org/W2015999626","https://openalex.org/W2093056734","https://openalex.org/W2111959010","https://openalex.org/W2143788833","https://openalex.org/W2163901668","https://openalex.org/W2176773914","https://openalex.org/W2521874673","https://openalex.org/W2592139554","https://openalex.org/W2801192398","https://openalex.org/W2802544858","https://openalex.org/W2883865130","https://openalex.org/W2884916346","https://openalex.org/W2911380382","https://openalex.org/W2934148492","https://openalex.org/W3000164190","https://openalex.org/W3093442658","https://openalex.org/W3192192562","https://openalex.org/W4205593870","https://openalex.org/W4239481137","https://openalex.org/W4247953052","https://openalex.org/W4250328251"],"related_works":["https://openalex.org/W2791839419","https://openalex.org/W2355760814","https://openalex.org/W2028225975","https://openalex.org/W2373670823","https://openalex.org/W2391213251","https://openalex.org/W2076078510","https://openalex.org/W2103565019","https://openalex.org/W2365843888","https://openalex.org/W2242259016","https://openalex.org/W2364639542"],"abstract_inverted_index":{"Abstract":[0],"We":[1,17],"extend":[2],"the":[3,6,14,27,30,38,49,60,63,73,86,92,103],"study":[4],"of":[5,48,59,72,85,91,106],"random":[7,21,39,74],"Hermite":[8],"second-order":[9],"ordinary":[10],"differential":[11],"equation":[12,28],"to":[13,78,101],"fractional":[15],"setting.":[16],"first":[18,87],"construct":[19,82],"a":[20,53],"generalized":[22],"power":[23],"series":[24],"that":[25],"solves":[26],"in":[29],"mean":[31,61],"square":[32],"sense":[33],"under":[34],"mild":[35],"hypotheses":[36],"on":[37],"inputs":[40],"(coefficients":[41],"and":[42,62,81],"initial":[43],"conditions).":[44],"From":[45],"this":[46],"representation":[47],"solution,":[50],"which":[51],"is":[52],"parametric":[54],"stochastic":[55],"process,":[56],"reliable":[57],"approximations":[58,84],"variance":[64],"are":[65,98],"explicitly":[66],"given.":[67],"Then,":[68],"we":[69],"take":[70],"advantage":[71],"variable":[75],"transformation":[76],"technique":[77],"go":[79],"further":[80],"convergent":[83],"probability":[88],"density":[89],"function":[90],"solution.":[93],"Finally,":[94],"several":[95],"numerically":[96],"simulations":[97],"carried":[99],"out":[100],"illustrate":[102],"broad":[104],"applicability":[105],"our":[107],"theoretical":[108],"findings.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2023-04-06T00:00:00"}
