{"id":"https://openalex.org/W3138238039","doi":"https://doi.org/10.3390/sym13030504","title":"Fractional (p,q)-Calculus on Finite Intervals and Some Integral Inequalities","display_name":"Fractional (p,q)-Calculus on Finite Intervals and Some Integral Inequalities","publication_year":2021,"publication_date":"2021-03-19","ids":{"openalex":"https://openalex.org/W3138238039","doi":"https://doi.org/10.3390/sym13030504","mag":"3138238039"},"language":"en","primary_location":{"id":"doi:10.3390/sym13030504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030504","pdf_url":"https://www.mdpi.com/2073-8994/13/3/504/pdf?version=1616572399","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/2073-8994/13/3/504/pdf?version=1616572399","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078708382","display_name":"Pheak Neang","orcid":"https://orcid.org/0000-0003-1323-9558"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Pheak Neang","raw_affiliation_strings":["Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089496116","display_name":"Kamsing Nonlaopon","orcid":"https://orcid.org/0000-0002-7469-5402"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Kamsing Nonlaopon","raw_affiliation_strings":["Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051443783","display_name":"Jessada Tariboon","orcid":"https://orcid.org/0000-0001-8185-3539"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Jessada Tariboon","raw_affiliation_strings":["Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086599287","display_name":"Sotiris K. Ntouyas","orcid":"https://orcid.org/0000-0002-7695-2118"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]},{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR","SA"],"is_corresponding":false,"raw_author_name":"Sotiris K. Ntouyas","raw_affiliation_strings":["Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]},{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089496116"],"corresponding_institution_ids":["https://openalex.org/I179193067"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.5974,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.95558854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"13","issue":"3","first_page":"504","last_page":"504"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9980999827384949,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9980999827384949,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9962000250816345,"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":0.9923999905586243,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7777696847915649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7248145341873169},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6301333904266357},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.47977739572525024},{"id":"https://openalex.org/keywords/time-scale-calculus","display_name":"Time-scale calculus","score":0.45677700638771057},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4479771852493286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3594871163368225},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35076943039894104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2940191626548767},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.22490549087524414}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7777696847915649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7248145341873169},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6301333904266357},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.47977739572525024},{"id":"https://openalex.org/C33695381","wikidata":"https://www.wikidata.org/wiki/Q7804838","display_name":"Time-scale calculus","level":3,"score":0.45677700638771057},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4479771852493286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3594871163368225},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35076943039894104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2940191626548767},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.22490549087524414},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13030504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030504","pdf_url":"https://www.mdpi.com/2073-8994/13/3/504/pdf?version=1616572399","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:f71ea1ed36d344ea98c974649f79205c","is_oa":true,"landing_page_url":"https://doaj.org/article/f71ea1ed36d344ea98c974649f79205c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 3, p 504 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/3/504/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13030504","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/sym13030504","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030504","pdf_url":"https://www.mdpi.com/2073-8994/13/3/504/pdf?version=1616572399","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3138238039.pdf","grobid_xml":"https://content.openalex.org/works/W3138238039.grobid-xml"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W339147017","https://openalex.org/W561050696","https://openalex.org/W566543047","https://openalex.org/W591568057","https://openalex.org/W1094476048","https://openalex.org/W1484588101","https://openalex.org/W1510348186","https://openalex.org/W1901426358","https://openalex.org/W1914025339","https://openalex.org/W1963574764","https://openalex.org/W1968997760","https://openalex.org/W1982446202","https://openalex.org/W1997566769","https://openalex.org/W1998776556","https://openalex.org/W2008052995","https://openalex.org/W2017083850","https://openalex.org/W2017498386","https://openalex.org/W2026780626","https://openalex.org/W2036044969","https://openalex.org/W2047602652","https://openalex.org/W2052295270","https://openalex.org/W2054550768","https://openalex.org/W2061810827","https://openalex.org/W2084392635","https://openalex.org/W2091675558","https://openalex.org/W2118017323","https://openalex.org/W2118360351","https://openalex.org/W2119337296","https://openalex.org/W2120430114","https://openalex.org/W2145453430","https://openalex.org/W2168136168","https://openalex.org/W2187394613","https://openalex.org/W2221985638","https://openalex.org/W2271531759","https://openalex.org/W2272977905","https://openalex.org/W2292214059","https://openalex.org/W2320016579","https://openalex.org/W2326886507","https://openalex.org/W2332309585","https://openalex.org/W2468704209","https://openalex.org/W2516871245","https://openalex.org/W2529427475","https://openalex.org/W2560344843","https://openalex.org/W2593622092","https://openalex.org/W2770148887","https://openalex.org/W2790013524","https://openalex.org/W2901042272","https://openalex.org/W2913053368","https://openalex.org/W2946976869","https://openalex.org/W2947101054","https://openalex.org/W2962753569","https://openalex.org/W2963059954","https://openalex.org/W2963103191","https://openalex.org/W2964984583","https://openalex.org/W3030308006","https://openalex.org/W3030652065","https://openalex.org/W3045056026","https://openalex.org/W3082259423","https://openalex.org/W3181508341","https://openalex.org/W3215201654","https://openalex.org/W4205678040","https://openalex.org/W4206216506","https://openalex.org/W4237451143","https://openalex.org/W4240644230","https://openalex.org/W4297813610","https://openalex.org/W6640942387","https://openalex.org/W6666193311","https://openalex.org/W6764066566","https://openalex.org/W6798376356"],"related_works":["https://openalex.org/W3168865234","https://openalex.org/W3162340984","https://openalex.org/W2098940483","https://openalex.org/W3084844296","https://openalex.org/W4312714491","https://openalex.org/W13827432","https://openalex.org/W2962784945","https://openalex.org/W4394988843","https://openalex.org/W1537973975","https://openalex.org/W4312960772"],"abstract_inverted_index":{"Fractional":[0],"q-calculus":[1],"has":[2],"been":[3],"investigated":[4],"and":[5,29],"applied":[6],"in":[7,12],"a":[8],"variety":[9],"of":[10],"fields":[11],"mathematical":[13],"areas":[14],"including":[15],"fractional":[16,24,37],"q-integral":[17],"inequalities.":[18],"In":[19,34],"this":[20],"paper,":[21],"we":[22],"study":[23],"(p,q)-calculus":[25],"on":[26,40],"finite":[27,41],"intervals":[28,42],"give":[30],"some":[31,36],"basic":[32],"properties.":[33],"particular,":[35],"(p,q)-integral":[38],"inequalities":[39],"are":[43],"proven.":[44]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-03-29T00:00:00"}