{"id":"https://openalex.org/W2121383182","doi":"https://doi.org/10.3390/axioms1030238","title":"A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions","display_name":"A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions","publication_year":2012,"publication_date":"2012-10-05","ids":{"openalex":"https://openalex.org/W2121383182","doi":"https://doi.org/10.3390/axioms1030238","mag":"2121383182"},"language":"en","primary_location":{"id":"doi:10.3390/axioms1030238","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms1030238","pdf_url":"https://www.mdpi.com/2075-1680/1/3/238/pdf?version=1349705477","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://www.mdpi.com/2075-1680/1/3/238/pdf?version=1349705477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079512627","display_name":"H. M. Srivastava","orcid":"https://orcid.org/0000-0002-9277-8092"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"H. M. Srivastava","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada"],"raw_orcid":"https://orcid.org/0000-0002-9277-8092","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009075908","display_name":"Rakesh K. Parmar","orcid":"https://orcid.org/0000-0001-9192-6535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rakesh K. Parmar","raw_affiliation_strings":["Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025350621","display_name":"Purnima Chopra","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Purnima Chopra","raw_affiliation_strings":["Department of Mathematics, Marudhar Engineering College, Raisar, NH-11 Jaipur Road, Bikaner 334001, Rajasthan, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Marudhar Engineering College, Raisar, NH-11 Jaipur Road, Bikaner 334001, Rajasthan, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079512627"],"corresponding_institution_ids":["https://openalex.org/I212119943"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":4.9448,"has_fulltext":true,"cited_by_count":71,"citation_normalized_percentile":{"value":0.9580015,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"1","issue":"3","first_page":"238","last_page":"258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9993000030517578,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9993000030517578,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7398712635040283},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6922654509544373},{"id":"https://openalex.org/keywords/hypergeometric-function","display_name":"Hypergeometric function","score":0.6622499227523804},{"id":"https://openalex.org/keywords/generalized-hypergeometric-function","display_name":"Generalized hypergeometric function","score":0.5862748622894287},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5637131333351135},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5250035524368286},{"id":"https://openalex.org/keywords/lauricella-hypergeometric-series","display_name":"Lauricella hypergeometric series","score":0.5236651301383972},{"id":"https://openalex.org/keywords/confluent-hypergeometric-function","display_name":"Confluent hypergeometric function","score":0.4912571310997009},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.45799902081489563},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39763593673706055},{"id":"https://openalex.org/keywords/hypergeometric-function-of-a-matrix-argument","display_name":"Hypergeometric function of a matrix argument","score":0.3380609154701233},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3128928244113922}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7398712635040283},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6922654509544373},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.6622499227523804},{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.5862748622894287},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5637131333351135},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5250035524368286},{"id":"https://openalex.org/C122343491","wikidata":"https://www.wikidata.org/wiki/Q3754612","display_name":"Lauricella hypergeometric series","level":5,"score":0.5236651301383972},{"id":"https://openalex.org/C148160416","wikidata":"https://www.wikidata.org/wiki/Q783948","display_name":"Confluent hypergeometric function","level":3,"score":0.4912571310997009},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.45799902081489563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39763593673706055},{"id":"https://openalex.org/C165175332","wikidata":"https://www.wikidata.org/wiki/Q5958021","display_name":"Hypergeometric function of a matrix argument","level":4,"score":0.3380609154701233},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3128928244113922},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/axioms1030238","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms1030238","pdf_url":"https://www.mdpi.com/2075-1680/1/3/238/pdf?version=1349705477","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:doaj.org/article:49242fad21aa4a5883769dbadc614e32","is_oa":true,"landing_page_url":"https://doaj.org/article/49242fad21aa4a5883769dbadc614e32","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 1, Iss 3, Pp 238-258 (2012)","raw_type":"article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/12171","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/12171","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dspace.library.uvic.ca:1828/12172","is_oa":false,"landing_page_url":"http://hdl.handle.net/1828/12172","pdf_url":null,"source":{"id":"https://openalex.org/S4306401509","display_name":"UVic\u2019s Research and Learning Repository (University of Victoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I212119943","host_organization_name":"University of Victoria","host_organization_lineage":["https://openalex.org/I212119943"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/2075-1680/1/3/238/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms1030238","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":"Axioms; Volume 1; Issue 3; Pages: 238-258","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms1030238","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms1030238","pdf_url":"https://www.mdpi.com/2075-1680/1/3/238/pdf?version=1349705477","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2121383182.pdf","grobid_xml":"https://content.openalex.org/works/W2121383182.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W193812311","https://openalex.org/W1485979810","https://openalex.org/W1499718604","https://openalex.org/W1584611818","https://openalex.org/W2002560278","https://openalex.org/W2009640650","https://openalex.org/W2040125866","https://openalex.org/W2042612461","https://openalex.org/W2056080408","https://openalex.org/W2060021847","https://openalex.org/W2068858251","https://openalex.org/W2089682264","https://openalex.org/W2098609738","https://openalex.org/W2299647821","https://openalex.org/W6667502983","https://openalex.org/W6672945336"],"related_works":["https://openalex.org/W4300001508","https://openalex.org/W2944115301","https://openalex.org/W3192609840","https://openalex.org/W2905308183","https://openalex.org/W1969129728","https://openalex.org/W4289106892","https://openalex.org/W2950344284","https://openalex.org/W2325544293","https://openalex.org/W1788447731","https://openalex.org/W2010866598"],"abstract_inverted_index":{"Recently,":[0],"an":[1],"extended":[2,24,42,50,64,89],"operator":[3,45,53,92],"of":[4,31,40],"fractional":[5,43,51,90],"derivative":[6,44,52,91],"related":[7],"to":[8,17,35,54],"a":[9,37],"generalized":[10,49,63,88],"Beta":[11],"function":[12],"was":[13],"used":[14],"in":[15,71],"order":[16],"obtain":[18],"some":[19],"generating":[20,59],"relations":[21,60],"involving":[22,82],"the":[23,41,48,62,83,87],"hypergeometric":[25,69],"functions":[26,70],"[1].":[27],"The":[28],"main":[29],"object":[30],"this":[32],"paper":[33],"is":[34],"present":[36],"further":[38],"generalization":[39],"and":[46,57,67,74,80,86],"apply":[47],"derive":[55],"linear":[56],"bilinear":[58],"for":[61],"Gauss,":[65],"Appell":[66],"Lauricella":[68],"one,":[72],"two":[73],"more":[75],"variables.":[76],"Some":[77],"other":[78],"properties":[79],"relationships":[81],"Mellin":[84],"transforms":[85],"are":[93],"also":[94],"given.":[95]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2016-06-24T00:00:00"}
