{"id":"https://openalex.org/W3153902684","doi":"https://doi.org/10.3390/sym13040669","title":"On the Generalized Laplace Transform","display_name":"On the Generalized Laplace Transform","publication_year":2021,"publication_date":"2021-04-13","ids":{"openalex":"https://openalex.org/W3153902684","doi":"https://doi.org/10.3390/sym13040669","mag":"3153902684"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040669","pdf_url":"https://www.mdpi.com/2073-8994/13/4/669/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/669/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113626780","display_name":"Paul Bosch","orcid":"https://orcid.org/0000-0001-5194-4173"},"institutions":[{"id":"https://openalex.org/I133599470","display_name":"Universidad del Desarrollo","ror":"https://ror.org/05y33vv83","country_code":"CL","type":"education","lineage":["https://openalex.org/I133599470"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Paul Bosch","raw_affiliation_strings":["Facultad de Ingenier\u00eda, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7550000, Chile"],"raw_orcid":"https://orcid.org/0000-0001-5194-4173","affiliations":[{"raw_affiliation_string":"Facultad de Ingenier\u00eda, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7550000, Chile","institution_ids":["https://openalex.org/I133599470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048745879","display_name":"Hector Carmenate","orcid":"https://orcid.org/0000-0002-1413-4873"},"institutions":[{"id":"https://openalex.org/I3130105584","display_name":"Universidad Aut\u00f3noma de Guerrero","ror":"https://ror.org/054tbkd46","country_code":"MX","type":"education","lineage":["https://openalex.org/I3130105584"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"H\u00e9ctor Jos\u00e9 Carmenate Garc\u00eda","raw_affiliation_strings":["Centro Acapulco, Facultad de Matem\u00e1tica, Universidad Aut\u00f3noma de Guerrero, Calle Chilpancingo, Acapulco de Ju\u00e1rez, Guerrero 39610, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro Acapulco, Facultad de Matem\u00e1tica, Universidad Aut\u00f3noma de Guerrero, Calle Chilpancingo, Acapulco de Ju\u00e1rez, Guerrero 39610, Mexico","institution_ids":["https://openalex.org/I3130105584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002592714","display_name":"Jos\u00e9 M. Rodr\u0131\u0301guez","orcid":"https://orcid.org/0000-0003-2851-7442"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Manuel Rodr\u00edguez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Legan\u00e9s, 28911 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-2851-7442","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Legan\u00e9s, 28911 Madrid, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027473542","display_name":"Jos\u00e9 M. Sigarreta","orcid":"https://orcid.org/0000-0003-4352-5109"},"institutions":[{"id":"https://openalex.org/I3130105584","display_name":"Universidad Aut\u00f3noma de Guerrero","ror":"https://ror.org/054tbkd46","country_code":"MX","type":"education","lineage":["https://openalex.org/I3130105584"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Mar\u00eda Sigarreta","raw_affiliation_strings":["Centro Acapulco, Facultad de Matem\u00e1tica, Universidad Aut\u00f3noma de Guerrero, Calle Chilpancingo, Acapulco de Ju\u00e1rez, Guerrero 39610, Mexico"],"raw_orcid":"https://orcid.org/0000-0003-4352-5109","affiliations":[{"raw_affiliation_string":"Centro Acapulco, Facultad de Matem\u00e1tica, Universidad Aut\u00f3noma de Guerrero, Calle Chilpancingo, Acapulco de Ju\u00e1rez, Guerrero 39610, Mexico","institution_ids":["https://openalex.org/I3130105584"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027473542"],"corresponding_institution_ids":["https://openalex.org/I3130105584"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9126,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.72464365,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"669","last_page":"669"},"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":0.9922999739646912,"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/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.8703100681304932},{"id":"https://openalex.org/keywords/inverse-laplace-transform","display_name":"Inverse Laplace transform","score":0.7797970771789551},{"id":"https://openalex.org/keywords/laplace-transform-applied-to-differential-equations","display_name":"Laplace transform applied to differential equations","score":0.7566080689430237},{"id":"https://openalex.org/keywords/two-sided-laplace-transform","display_name":"Two-sided Laplace transform","score":0.7503234148025513},{"id":"https://openalex.org/keywords/laplace\u2013stieltjes-transform","display_name":"Laplace\u2013Stieltjes transform","score":0.7106202840805054},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.7072110176086426},{"id":"https://openalex.org/keywords/mellin-transform","display_name":"Mellin transform","score":0.6899673938751221},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.6798034310340881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6389085054397583},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5229706764221191},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46149834990501404},{"id":"https://openalex.org/keywords/greens-function-for-the-three-variable-laplace-equation","display_name":"Green's function for the three-variable Laplace equation","score":0.45090287923812866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44495996832847595},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.35365989804267883},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.16310042142868042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14355146884918213}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.8703100681304932},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.7797970771789551},{"id":"https://openalex.org/C194330524","wikidata":"https://www.wikidata.org/wiki/Q2858841","display_name":"Laplace transform applied to differential equations","level":3,"score":0.7566080689430237},{"id":"https://openalex.org/C10288518","wikidata":"https://www.wikidata.org/wiki/Q1785576","display_name":"Two-sided Laplace transform","level":5,"score":0.7503234148025513},{"id":"https://openalex.org/C141255357","wikidata":"https://www.wikidata.org/wiki/Q3997728","display_name":"Laplace\u2013Stieltjes transform","level":5,"score":0.7106202840805054},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.7072110176086426},{"id":"https://openalex.org/C199874217","wikidata":"https://www.wikidata.org/wiki/Q606934","display_name":"Mellin transform","level":3,"score":0.6899673938751221},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.6798034310340881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6389085054397583},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5229706764221191},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46149834990501404},{"id":"https://openalex.org/C208067445","wikidata":"https://www.wikidata.org/wiki/Q5602166","display_name":"Green's function for the three-variable Laplace equation","level":4,"score":0.45090287923812866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44495996832847595},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.35365989804267883},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.16310042142868042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14355146884918213},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13040669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040669","pdf_url":"https://www.mdpi.com/2073-8994/13/4/669/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:52de551863464201ad4142c4a4820ef2","is_oa":true,"landing_page_url":"https://doaj.org/article/52de551863464201ad4142c4a4820ef2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 4, p 669 (2021)","raw_type":"article"},{"id":"pmh:oai:e-archivo.uc3m.es:10016/33496","is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/33496","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/669/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13040669","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040669","pdf_url":"https://www.mdpi.com/2073-8994/13/4/669/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3153902684.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1511979834","https://openalex.org/W1585552811","https://openalex.org/W1869690418","https://openalex.org/W1997479492","https://openalex.org/W2063067239","https://openalex.org/W2080931732","https://openalex.org/W2083559699","https://openalex.org/W2115673781","https://openalex.org/W2472805732","https://openalex.org/W2486175508","https://openalex.org/W2607641746","https://openalex.org/W2747750973","https://openalex.org/W2762918090","https://openalex.org/W2772643525","https://openalex.org/W2790400853","https://openalex.org/W2921804090","https://openalex.org/W2943514272","https://openalex.org/W2953308073","https://openalex.org/W2953783031","https://openalex.org/W2963311973","https://openalex.org/W2963520255","https://openalex.org/W2981587143","https://openalex.org/W3023434962","https://openalex.org/W3098505584","https://openalex.org/W6635020632","https://openalex.org/W6743182253","https://openalex.org/W6764672550","https://openalex.org/W6769696895","https://openalex.org/W6804958523"],"related_works":["https://openalex.org/W193874820","https://openalex.org/W3022275705","https://openalex.org/W3166878184","https://openalex.org/W4389482554","https://openalex.org/W3027042443","https://openalex.org/W2484425659","https://openalex.org/W1996624184","https://openalex.org/W586165726","https://openalex.org/W4247377967","https://openalex.org/W1982907413"],"abstract_inverted_index":{"In":[0,37],"this":[1,25,44,62],"paper":[2],"we":[3,20,52],"introduce":[4],"a":[5,14],"generalized":[6,45,56],"Laplace":[7,46],"transform":[8,47,63],"in":[9],"order":[10],"to":[11,69],"work":[12],"with":[13,54],"very":[15],"general":[16],"fractional":[17,71],"derivative,":[18],"and":[19,34,64],"obtain":[21],"the":[22,31,39,55],"properties":[23,66],"of":[24,41],"new":[26],"transform.":[27],"We":[28],"also":[29],"include":[30],"corresponding":[32],"convolution":[33,42],"inverse":[35],"formula.":[36],"particular,":[38],"definition":[40],"for":[43],"improves":[48],"previous":[49],"results.":[50],"Additionally,":[51],"deal":[53],"harmonic":[57],"oscillator":[58],"equation,":[59],"showing":[60],"that":[61],"its":[65],"allow":[67],"one":[68],"solve":[70],"differential":[72],"equations.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
