{"id":"https://openalex.org/W3214938231","doi":"https://doi.org/10.3934/math.2022177","title":"Some new generalized $ \\kappa $\u2013fractional Hermite\u2013Hadamard\u2013Mercer type integral inequalities and their applications","display_name":"Some new generalized $ \\kappa $\u2013fractional Hermite\u2013Hadamard\u2013Mercer type integral inequalities and their applications","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3214938231","doi":"https://doi.org/10.3934/math.2022177","mag":"3214938231"},"language":"en","primary_location":{"id":"doi:10.3934/math.2022177","doi":"https://doi.org/10.3934/math.2022177","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2022177","pdf_url":null,"source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3934/math.2022177","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066464647","display_name":"Miguel Jos\u00e9 Vivas Cortez","orcid":"https://orcid.org/0000-0002-1567-0264","observed_orcids":["https://orcid.org/0000-0002-1567-0264"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miguel Vivas-Cortez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035904409","display_name":"Muhammad Uzair Awan","orcid":"https://orcid.org/0000-0002-1019-9485","observed_orcids":["https://orcid.org/0000-0002-1019-9485"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Uzair Awan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069757223","display_name":"Muhammad Zakria Javed","orcid":"https://orcid.org/0000-0001-5212-6252","observed_orcids":["https://orcid.org/0000-0001-5212-6252"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Zakria Javed","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007318507","display_name":"Artion Kashuri","orcid":"https://orcid.org/0000-0003-0115-3079","observed_orcids":["https://orcid.org/0000-0003-0115-3079"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Artion Kashuri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087578803","display_name":"Muhammad Aslam Noor","orcid":"https://orcid.org/0000-0001-6105-2435","observed_orcids":["https://orcid.org/0000-0001-6105-2435"]},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]},{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]},{"id":"https://openalex.org/I39398033","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51","country_code":"EC","type":"education","lineage":["https://openalex.org/I39398033"]}],"countries":["EC","PK"],"is_corresponding":true,"raw_author_name":"Muhammad Aslam Noor","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","Department of Mathematics, Faculty of Technical Science, University","Department of Mathematics, Government College University, Faisalabad, Pakistan","Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical Science, University","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I194348271"]},{"raw_affiliation_string":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador","institution_ids":["https://openalex.org/I39398033"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060630057","display_name":"Khalida Inayat Noor","orcid":"https://orcid.org/0000-0002-5000-3870","observed_orcids":["https://orcid.org/0000-0002-5000-3870"]},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]},{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]},{"id":"https://openalex.org/I39398033","display_name":"Pontificia Universidad Cat\u00f3lica del Ecuador","ror":"https://ror.org/02qztda51","country_code":"EC","type":"education","lineage":["https://openalex.org/I39398033"]}],"countries":["EC","PK"],"is_corresponding":false,"raw_author_name":"Khalida Inayat Noor","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","Department of Mathematics, Faculty of Technical Science, University","Department of Mathematics, Government College University, Faisalabad, Pakistan","Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical Science, University","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I194348271"]},{"raw_affiliation_string":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador","institution_ids":["https://openalex.org/I39398033"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087578803"],"corresponding_institution_ids":["https://openalex.org/I16076960","https://openalex.org/I194348271","https://openalex.org/I39398033"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":2.0999,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87512267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"7","issue":"2","first_page":"3203","last_page":"3220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"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":1.0,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.0,"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/generalized-fractional-integrals","display_name":"generalized fractional integrals","score":0.7139999866485596},{"id":"https://openalex.org/keywords/integral-identities","display_name":"integral identities","score":0.9300000071525574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8023544549942017},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.7429784536361694},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7163835167884827},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.601814329624176},{"id":"https://openalex.org/C2778724333","wikidata":"https://www.wikidata.org/wiki/Q14401","display_name":"Kappa","level":2,"score":0.5239073038101196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5163356065750122},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4835517108440399},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46406516432762146},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.44986701011657715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.327739953994751},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0709749162197113},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0485510528087616},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/math.2022177","doi":"https://doi.org/10.3934/math.2022177","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2022177","pdf_url":null,"source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5dfc22f5255e4576960fcc961e4eac90","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/5dfc22f5255e4576960fcc961e4eac90","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,"listed_in":[],"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":"AIMS Mathematics, Vol 7, Iss 2, Pp 3203-3220 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/math.2022177","doi":"https://doi.org/10.3934/math.2022177","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2022177","pdf_url":null,"source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1553338987","https://openalex.org/W2006458314","https://openalex.org/W2133842309","https://openalex.org/W2185892409","https://openalex.org/W2314878366","https://openalex.org/W2603194489","https://openalex.org/W2970542527","https://openalex.org/W2973077357","https://openalex.org/W2988451101","https://openalex.org/W3000320805","https://openalex.org/W3015640008","https://openalex.org/W3020810561","https://openalex.org/W3035002262","https://openalex.org/W3037530917","https://openalex.org/W3045865188","https://openalex.org/W3118906034","https://openalex.org/W3173191086","https://openalex.org/W3182173111","https://openalex.org/W3209317593","https://openalex.org/W4205290186","https://openalex.org/W4242820328"],"related_works":["https://openalex.org/W2593268940","https://openalex.org/W3161241424","https://openalex.org/W7169567701","https://openalex.org/W7135189823","https://openalex.org/W7106850564","https://openalex.org/W2790683667","https://openalex.org/W3165575330","https://openalex.org/W4407166153","https://openalex.org/W3020810561","https://openalex.org/W4410396990"],"abstract_inverted_index":{"In":[0,67],"this":[1],"paper,":[2],"we":[3,20,37],"have":[4,21,38],"established":[5],"some":[6,40,60,77],"new":[7,24,41],"Hermite\u2013Hadamard\u2013Mercer":[8,44],"type":[9,45],"of":[10,43,73,82],"inequalities":[11],"by":[12],"using":[13],"$":[14,47],"{\\kappa}":[15,48],"$\u2013Riemann\u2013Liouville":[16,49],"fractional":[17,50],"integrals.":[18,51],"Moreover,":[19],"derived":[22],"two":[23],"integral":[25],"identities":[26,33],"as":[27,34,65,96],"auxiliary":[28,35],"results.":[29],"From":[30],"the":[31,71,90],"applied":[32],"results,":[36,76],"obtained":[39],"variants":[42],"via":[46],"Several":[52],"special":[53,80],"cases":[54],"are":[55,63,94],"deduced":[56],"in":[57],"detail":[58],"and":[59,86],"know":[61],"results":[62],"recaptured":[64],"well.":[66,97],"order":[68],"to":[69],"illustrate":[70],"efficiency":[72],"our":[74],"main":[75],"applications":[78],"regarding":[79],"means":[81],"positive":[83],"real":[84],"numbers":[85],"error":[87],"estimations":[88],"for":[89],"trapezoidal":[91],"quadrature":[92],"formula":[93],"provided":[95]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3}],"updated_date":"2026-09-25T08:18:29.962427","created_date":"2021-12-06T00:00:00"}
