{"id":"https://openalex.org/W3198326285","doi":"https://doi.org/10.1155/2021/9260828","title":"Fractional Hermite\u2013Jensen\u2013Mercer Integral Inequalities with respect to Another Function and Application","display_name":"Fractional Hermite\u2013Jensen\u2013Mercer Integral Inequalities with respect to Another Function and Application","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3198326285","doi":"https://doi.org/10.1155/2021/9260828","mag":"3198326285"},"language":"en","primary_location":{"id":"doi:10.1155/2021/9260828","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9260828","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9260828.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2021/9260828.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024489529","display_name":"Saad Ihsan Butt","orcid":"https://orcid.org/0000-0001-7192-8269"},"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"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saad Ihsan Butt","raw_affiliation_strings":["COMSATs University Islamabad, Lahore Campus, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7192-8269","affiliations":[{"raw_affiliation_string":"COMSATs University Islamabad, Lahore Campus, Lahore, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101745977","display_name":"Muhammad Umar","orcid":"https://orcid.org/0000-0001-9911-1111"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Umar","raw_affiliation_strings":["Afro-Asian Institute, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-9911-1111","affiliations":[{"raw_affiliation_string":"Afro-Asian Institute, Lahore, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065052393","display_name":"Khuram Ali Khan","orcid":"https://orcid.org/0000-0002-3468-2295"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khuram Ali Khan","raw_affiliation_strings":["Department of Mathematics, University of Sargdha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3468-2295","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargdha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007318507","display_name":"Artion Kashuri","orcid":"https://orcid.org/0000-0003-0115-3079"},"institutions":[{"id":"https://openalex.org/I3130420675","display_name":"University of Vlora \"Ismail Qemali\"","ror":"https://ror.org/05ger6s34","country_code":"AL","type":"education","lineage":["https://openalex.org/I3130420675"]}],"countries":["AL"],"is_corresponding":false,"raw_author_name":"Artion Kashuri","raw_affiliation_strings":["Department of Mathematics, Faculty of Technical Science, University \"Ismail Qemali\", 9400 Vlor, Albania","Department of Mathematics, Faculty of Technical Science, University \"Ismail Qemali\", 9400 Vlor\u00eb, Albania"],"raw_orcid":"https://orcid.org/0000-0003-0115-3079","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical Science, University \"Ismail Qemali\", 9400 Vlor, Albania","institution_ids":["https://openalex.org/I3130420675"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Technical Science, University \"Ismail Qemali\", 9400 Vlor\u00eb, Albania","institution_ids":["https://openalex.org/I3130420675"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057055069","display_name":"Homan Emadifar","orcid":"https://orcid.org/0000-0002-8034-1475"},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Homan Emadifar","raw_affiliation_strings":["Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran"],"raw_orcid":"https://orcid.org/0000-0002-8034-1475","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran","institution_ids":["https://openalex.org/I4210089026"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5057055069"],"corresponding_institution_ids":["https://openalex.org/I4210089026"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":3.9621,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.9463451,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980000257492065,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9927999973297119,"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/mathematics","display_name":"Mathematics","score":0.7625806927680969},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6481478214263916},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5741636753082275},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5437728762626648},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5428292155265808},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5224272608757019},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4460141956806183},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.4325745701789856},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4294111728668213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3402109146118164},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3379841148853302},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25243711471557617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7625806927680969},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6481478214263916},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5741636753082275},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5437728762626648},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5428292155265808},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5224272608757019},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4460141956806183},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.4325745701789856},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4294111728668213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3402109146118164},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3379841148853302},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25243711471557617},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2021/9260828","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9260828","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9260828.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:895890b21b824d3dadcb9726c03bc4f8","is_oa":true,"landing_page_url":"https://doaj.org/article/895890b21b824d3dadcb9726c03bc4f8","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":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/9260828","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/9260828","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/9260828.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5899999737739563}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3198326285.pdf","grobid_xml":"https://content.openalex.org/works/W3198326285.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1553338987","https://openalex.org/W1584611818","https://openalex.org/W1987113198","https://openalex.org/W2032712686","https://openalex.org/W2063067239","https://openalex.org/W2128181058","https://openalex.org/W2145886492","https://openalex.org/W2310545763","https://openalex.org/W2483375472","https://openalex.org/W2506586217","https://openalex.org/W2551053413","https://openalex.org/W2596323328","https://openalex.org/W2603194489","https://openalex.org/W2613734495","https://openalex.org/W2919162022","https://openalex.org/W2963138266","https://openalex.org/W2963311973","https://openalex.org/W2963670184","https://openalex.org/W2979628066","https://openalex.org/W2990568942","https://openalex.org/W3012221704","https://openalex.org/W3033931532","https://openalex.org/W3035002262","https://openalex.org/W3035692153","https://openalex.org/W3046637225","https://openalex.org/W3087013225","https://openalex.org/W3087475508","https://openalex.org/W3094785456","https://openalex.org/W3096045933","https://openalex.org/W3105863746","https://openalex.org/W3147458306","https://openalex.org/W4245151940","https://openalex.org/W4300694852","https://openalex.org/W6735588220"],"related_works":["https://openalex.org/W2949862693","https://openalex.org/W2924823355","https://openalex.org/W2112350011","https://openalex.org/W2510868853","https://openalex.org/W2269001854","https://openalex.org/W2314757131","https://openalex.org/W1953770356","https://openalex.org/W2409606037","https://openalex.org/W3008501853","https://openalex.org/W2945464711"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"authors":[3],"prove":[4],"new":[5],"variants":[6],"of":[7,78],"Hermite\u2013Jensen\u2013Mercer":[8,53],"type":[9,54],"inequalities":[10],"using":[11,73],"\u03c8":[12,28],"\u2013Riemann\u2013Liouville":[13,29],"fractional":[14,30,52],"integrals":[15],"with":[16],"respect":[17],"to":[18,46],"another":[19],"function":[20,38,77],"via":[21],"convexity.":[22],"We":[23],"establish":[24],"generalized":[25],"identities":[26],"involving":[27],"integral":[31],"pertaining":[32],"first":[33,80],"and":[34,41],"twice":[35],"differentiable":[36],"convex":[37],"\u03bb":[39],",":[40],"these":[42],"will":[43],"be":[44],"used":[45],"derive":[47],"novel":[48],"estimates":[49],"for":[50],"some":[51],"inequalities.":[55],"Some":[56],"known":[57],"results":[58,63,72],"are":[59],"recaptured":[60],"from":[61,70],"our":[62,71],"as":[64,84],"special":[65],"cases.":[66],"Finally,":[67],"an":[68],"application":[69],"the":[74,79],"modified":[75],"Bessel":[76],"kind":[81],"is":[82],"established":[83],"well.":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}