{"id":"https://openalex.org/W4410231292","doi":"https://doi.org/10.3390/axioms14050358","title":"Hybrid Integral Inequalities on Fractal Set","display_name":"Hybrid Integral Inequalities on Fractal Set","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W4410231292","doi":"https://doi.org/10.3390/axioms14050358"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14050358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050358","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/axioms14050358","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041971964","display_name":"Badreddine Meftah","orcid":"https://orcid.org/0000-0002-0156-7864"},"institutions":[{"id":"https://openalex.org/I4210097536","display_name":"University of Guelma","ror":"https://ror.org/00xe6p546","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210097536"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Badreddine Meftah","raw_affiliation_strings":["Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria"],"raw_orcid":"https://orcid.org/0000-0002-0156-7864","affiliations":[{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Facuty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014836528","display_name":"Wedad Saleh","orcid":"https://orcid.org/0000-0003-0600-2624"},"institutions":[{"id":"https://openalex.org/I23075662","display_name":"Taibah University","ror":"https://ror.org/01xv1nn60","country_code":"SA","type":"education","lineage":["https://openalex.org/I23075662"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Wedad Saleh","raw_affiliation_strings":["Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0600-2624","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 42210, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035904409","display_name":"Muhammad Uzair Awan","orcid":"https://orcid.org/0000-0002-1019-9485"},"institutions":[{"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"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Uzair Awan","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1019-9485","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010742167","display_name":"Loredana Ciurdariu","orcid":"https://orcid.org/0000-0002-1234-7939"},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Loredana Ciurdariu","raw_affiliation_strings":["Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania"],"raw_orcid":"https://orcid.org/0000-0002-1234-7939","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania","institution_ids":["https://openalex.org/I3122695212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045622615","display_name":"Abdelghani Lakhdari","orcid":"https://orcid.org/0000-0003-2943-2678"},"institutions":[{"id":"https://openalex.org/I51826884","display_name":"Kocaeli \u00dcniversitesi","ror":"https://ror.org/0411seq30","country_code":"TR","type":"education","lineage":["https://openalex.org/I51826884"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Abdelghani Lakhdari","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, T\u00fcrkiye","Laboratory of Energy Systems Technology, Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria"],"raw_orcid":"https://orcid.org/0000-0003-2943-2678","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, T\u00fcrkiye","institution_ids":["https://openalex.org/I51826884"]},{"raw_affiliation_string":"Laboratory of Energy Systems Technology, Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13126203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"5","first_page":"358","last_page":"358"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9994000196456909,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9994000196456909,"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/T11564","display_name":"Mathematical Inequalities and Applications","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/T11191","display_name":"Mathematical functions and polynomials","score":0.986299991607666,"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/fractal","display_name":"Fractal","score":0.6481862664222717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5659018754959106},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5381468534469604},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5245350003242493},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3683151602745056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3589378595352173},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33285659551620483},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32463592290878296},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24102574586868286}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6481862664222717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5659018754959106},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5381468534469604},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5245350003242493},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3683151602745056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3589378595352173},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33285659551620483},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32463592290878296},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24102574586868286},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14050358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050358","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:d5c41649-5c38-4dca-9f34-c64dea75718f","is_oa":false,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/d5c41649-5c38-4dca-9f34-c64dea75718f/oai","pdf_url":null,"source":{"id":"https://openalex.org/S7407055291","display_name":"Kocaeli \u00dcniversitesi - AVES\u0130S","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:5e96380f703443fdaf135ed34e40048b","is_oa":true,"landing_page_url":"https://doaj.org/article/5e96380f703443fdaf135ed34e40048b","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 14, Iss 5, p 358 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14050358","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050358","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W656501022","https://openalex.org/W1992457560","https://openalex.org/W2033302765","https://openalex.org/W2118851328","https://openalex.org/W2134436730","https://openalex.org/W2144521565","https://openalex.org/W2955550363","https://openalex.org/W2965670039","https://openalex.org/W2990950491","https://openalex.org/W2995028956","https://openalex.org/W3033880049","https://openalex.org/W3047289956","https://openalex.org/W3049545490","https://openalex.org/W3081272763","https://openalex.org/W3110288819","https://openalex.org/W3116843943","https://openalex.org/W3142469695","https://openalex.org/W3189744089","https://openalex.org/W3195607710","https://openalex.org/W4205102926","https://openalex.org/W4220931737","https://openalex.org/W4238652859","https://openalex.org/W4283730830","https://openalex.org/W4293255234","https://openalex.org/W4320151977","https://openalex.org/W4328050728","https://openalex.org/W4385197388","https://openalex.org/W4385397292","https://openalex.org/W4388645657","https://openalex.org/W4389833165","https://openalex.org/W4393276281","https://openalex.org/W4399439907","https://openalex.org/W4399752235","https://openalex.org/W4400741895","https://openalex.org/W4401193472","https://openalex.org/W4402763686","https://openalex.org/W4403137947","https://openalex.org/W4403658776","https://openalex.org/W4404923207","https://openalex.org/W4407370162","https://openalex.org/W6680097940","https://openalex.org/W6799563300","https://openalex.org/W6849711141","https://openalex.org/W6870791243"],"related_works":["https://openalex.org/W2013332237","https://openalex.org/W1522259561","https://openalex.org/W4313556169","https://openalex.org/W2295517574","https://openalex.org/W2380221404","https://openalex.org/W2373248682","https://openalex.org/W1968456887","https://openalex.org/W2225738837","https://openalex.org/W944314213","https://openalex.org/W2156263007"],"abstract_inverted_index":{"In":[0,61],"this":[1,38],"study,":[2],"we":[3,41,103],"introduce":[4],"a":[5,57,81,105],"new":[6,44],"hybrid":[7],"identity":[8],"that":[9,108,121],"effectively":[10],"combines":[11],"Newton\u2013Cotes":[12],"and":[13,27,30,80],"Gauss":[14],"quadrature,":[15],"allowing":[16],"us":[17],"to":[18,63],"recover":[19],"well-known":[20],"formulas":[21],"such":[22],"as":[23],"Simpson\u2019s":[24],"second":[25],"rule":[26],"the":[28,73,76,85,93,110,113],"left-":[29],"right-Radau":[31],"two-point":[32],"rules,":[33],"among":[34],"others.":[35],"Building":[36],"upon":[37],"flexible":[39],"framework,":[40],"establish":[42],"several":[43],"biparametrized":[45],"fractal":[46],"integral":[47],"inequalities":[48],"for":[49],"functions":[50],"whose":[51],"local":[52,67],"fractional":[53,68],"derivatives":[54],"are":[55,89],"of":[56,84,95,112],"generalized":[58,96],"convex":[59],"type.":[60],"addition":[62],"employing":[64],"tools":[65],"from":[66],"calculus,":[69],"our":[70,100],"approach":[71],"utilizes":[72],"H\u00f6lder":[74],"inequality,":[75,79],"power":[77],"mean":[78],"refined":[82],"version":[83],"latter.":[86],"Further":[87],"results":[88],"also":[90],"derived":[91],"using":[92],"concept":[94],"concavity.":[97],"To":[98],"support":[99],"theoretical":[101],"findings,":[102],"provide":[104],"graphical":[106],"example":[107],"illustrates":[109],"validity":[111],"obtained":[114],"results,":[115],"along":[116],"with":[117],"some":[118],"practical":[119],"applications":[120],"demonstrate":[122],"their":[123],"effectiveness.":[124]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}