{"id":"https://openalex.org/W4402235460","doi":"https://doi.org/10.3390/axioms13090600","title":"Fourier Series Related to p-Trigonometric Functions","display_name":"Fourier Series Related to p-Trigonometric Functions","publication_year":2024,"publication_date":"2024-09-04","ids":{"openalex":"https://openalex.org/W4402235460","doi":"https://doi.org/10.3390/axioms13090600"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13090600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090600","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms13090600","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5095778500","display_name":"Ali Hamzah Alibrahim","orcid":"https://orcid.org/0009-0002-8333-6097"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]},{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB","SA"],"is_corresponding":false,"raw_author_name":"Ali Hamzah Alibrahim","raw_affiliation_strings":["Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK","Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0002-8333-6097","affiliations":[{"raw_affiliation_string":"Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK","institution_ids":["https://openalex.org/I23923803"]},{"raw_affiliation_string":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074019305","display_name":"Saptarshi Das","orcid":"https://orcid.org/0000-0002-8394-5303"},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Saptarshi Das","raw_affiliation_strings":["Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK","Institute for Data Science and Artificial Intelligence, University of Exeter, North Park Road, Exeter EX4 4QE, UK"],"raw_orcid":"https://orcid.org/0000-0002-8394-5303","affiliations":[{"raw_affiliation_string":"Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Penryn TR10 9FE, UK","institution_ids":["https://openalex.org/I23923803"]},{"raw_affiliation_string":"Institute for Data Science and Artificial Intelligence, University of Exeter, North Park Road, Exeter EX4 4QE, UK","institution_ids":["https://openalex.org/I23923803"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22162114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"9","first_page":"600","last_page":"600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9945999979972839,"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/T12504","display_name":"Mathematics and Applications","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/fourier-series","display_name":"Fourier series","score":0.6682473421096802},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6121577620506287},{"id":"https://openalex.org/keywords/trigonometric-series","display_name":"Trigonometric series","score":0.5857881307601929},{"id":"https://openalex.org/keywords/fourier-sine-and-cosine-series","display_name":"Fourier sine and cosine series","score":0.5460876822471619},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.4456169605255127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4405456483364105},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.3758060336112976},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.37360018491744995},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3354909420013428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33396297693252563},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2304776906967163},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.13446304202079773},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.07212582230567932},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.06095084547996521}],"concepts":[{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6682473421096802},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6121577620506287},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.5857881307601929},{"id":"https://openalex.org/C56552780","wikidata":"https://www.wikidata.org/wiki/Q5475798","display_name":"Fourier sine and cosine series","level":5,"score":0.5460876822471619},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.4456169605255127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4405456483364105},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3758060336112976},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.37360018491744995},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3354909420013428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33396297693252563},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2304776906967163},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.13446304202079773},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.07212582230567932},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06095084547996521},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms13090600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090600","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:ore.exeter.ac.uk:10871/137338","is_oa":true,"landing_page_url":"http://hdl.handle.net/10871/137338","pdf_url":"https://ore.exeter.ac.uk/articles/journal_contribution/Fourier_Series_Related_to_p-Trigonometric_Functions/29811491/1/files/56857715.pdf","source":{"id":"https://openalex.org/S4306401998","display_name":"Open Research Exeter (University of Exeter)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23923803","host_organization_name":"University of Exeter","host_organization_lineage":["https://openalex.org/I23923803"],"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":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:43af3dba4d5a4c2d8298e91ef15163f7","is_oa":true,"landing_page_url":"https://doaj.org/article/43af3dba4d5a4c2d8298e91ef15163f7","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":"Axioms, Vol 13, Iss 9, p 600 (2024)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/29811491","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Fourier_Series_Related_to_p-Trigonometric_Functions/29811491","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms13090600","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13090600","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313486","display_name":"Saudi Arabia Cultural Bureau in London","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W47919846","https://openalex.org/W2040356516","https://openalex.org/W2261404145","https://openalex.org/W2326492432","https://openalex.org/W2514270350","https://openalex.org/W2809423184","https://openalex.org/W2895283200","https://openalex.org/W2904484735","https://openalex.org/W3008614407","https://openalex.org/W3091559907","https://openalex.org/W3169646149","https://openalex.org/W4211006520","https://openalex.org/W4292024750","https://openalex.org/W4394952412","https://openalex.org/W4401538225"],"related_works":["https://openalex.org/W4245037018","https://openalex.org/W4234757101","https://openalex.org/W2370547058","https://openalex.org/W2625700408","https://openalex.org/W3105828693","https://openalex.org/W2751880894","https://openalex.org/W2012991594","https://openalex.org/W4245419540","https://openalex.org/W1990381924","https://openalex.org/W2094684004"],"abstract_inverted_index":{"In":[0,48],"this":[1,32],"paper,":[2],"we":[3,53,83],"introduce":[4],"the":[5,13,24,56,59,62,71,79,89,92,115],"concept":[6],"of":[7,31,43,58,61,67,74,91,117],"generalized":[8,25,93,102],"Fourier":[9,103],"series,":[10],"generated":[11],"by":[12],"p-trigonometric":[14,68],"functions,":[15],"namely":[16],"cosp":[17],"and":[18,45],"sinp,":[19],"recently":[20],"introduced":[21],"related":[22],"to":[23,35,50,77,87,108],"complex":[26],"numbers":[27],"systems.":[28],"The":[29,101],"aim":[30],"study":[33],"is":[34],"represent":[36],"a":[37,41,98,118],"periodic":[38],"signal":[39],"as":[40],"sum":[42],"p-sine":[44],"p-cosine":[46],"functions.":[47],"order":[49],"achieve":[51],"this,":[52],"first":[54],"present":[55],"integrals":[57,86],"product":[60],"same":[63],"or":[64],"different":[65],"family":[66],"functions":[69,76],"over":[70],"full":[72],"period":[73],"these":[75,85],"understand":[78],"orthogonality":[80],"properties.":[81],"Next,":[82],"use":[84],"derive":[88],"coefficients":[90],"p-Fourier":[94],"series":[95,104],"along":[96],"with":[97,125],"few":[99],"examples.":[100],"can":[105],"be":[106],"used":[107],"expand":[109],"an":[110],"arbitrary":[111],"forcing":[112],"function":[113],"in":[114],"solution":[116],"non-homogeneous":[119],"linear":[120],"ordinary":[121],"differential":[122],"equation":[123],"(ODE)":[124],"constant":[126],"coefficients.":[127]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
