{"id":"https://openalex.org/W4391614341","doi":"https://doi.org/10.3390/sym16020196","title":"On Conformable Fractional Milne-Type Inequalities","display_name":"On Conformable Fractional Milne-Type Inequalities","publication_year":2024,"publication_date":"2024-02-07","ids":{"openalex":"https://openalex.org/W4391614341","doi":"https://doi.org/10.3390/sym16020196"},"language":"en","primary_location":{"id":"doi:10.3390/sym16020196","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020196","pdf_url":"https://www.mdpi.com/2073-8994/16/2/196/pdf?version=1707303183","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/2073-8994/16/2/196/pdf?version=1707303183","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100829821","display_name":"Rui Ying","orcid":null},"institutions":[{"id":"https://openalex.org/I10496686","display_name":"Shangrao Normal University","ror":"https://ror.org/024qkwh22","country_code":"CN","type":"education","lineage":["https://openalex.org/I10496686"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Ying","raw_affiliation_strings":["Basic Department, Shangrao Preschool Education College, Shangrao 334001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basic Department, Shangrao Preschool Education College, Shangrao 334001, China","institution_ids":["https://openalex.org/I10496686"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045622615","display_name":"Abdelghani Lakhdari","orcid":"https://orcid.org/0000-0003-2943-2678"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdelghani Lakhdari","raw_affiliation_strings":["Departement CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria"],"raw_orcid":"https://orcid.org/0000-0003-2943-2678","affiliations":[{"raw_affiliation_string":"Departement CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103233498","display_name":"Hongyan Xu","orcid":"https://orcid.org/0009-0007-0648-3508"},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyan Xu","raw_affiliation_strings":["School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China"],"raw_orcid":"https://orcid.org/0009-0007-0648-3508","affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China","institution_ids":["https://openalex.org/I4210119042"]}]},{"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, Taibah University, Al Medinah 42353, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taibah University, Al Medinah 42353, Saudi Arabia","institution_ids":["https://openalex.org/I23075662"]}]},{"author_position":"last","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":true,"raw_author_name":"Badreddine Meftah","raw_affiliation_strings":["Laboratory of Analysis and Control of Differential Equations \u2018ACED\u2019, Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria","Laboratory of Analysis and Control of Differential Equations 'ACED', Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \u2018ACED\u2019, Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]},{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations 'ACED', Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5041971964"],"corresponding_institution_ids":["https://openalex.org/I4210097536"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":17.3064,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.99716116,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"16","issue":"2","first_page":"196","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.992900013923645,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9878000020980835,"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/conformable-matrix","display_name":"Conformable matrix","score":0.973800778388977},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6435143947601318},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5821307897567749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5454803109169006},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5347836017608643},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.46072083711624146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46068787574768066},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.43358325958251953},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.402326762676239},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38153862953186035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18433451652526855},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11473968625068665}],"concepts":[{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.973800778388977},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6435143947601318},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5821307897567749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5454803109169006},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5347836017608643},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.46072083711624146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46068787574768066},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.43358325958251953},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.402326762676239},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38153862953186035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18433451652526855},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11473968625068665},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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":3,"locations":[{"id":"doi:10.3390/sym16020196","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020196","pdf_url":"https://www.mdpi.com/2073-8994/16/2/196/pdf?version=1707303183","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:896e7a2f-0e00-4e0b-8771-8455859d4424","is_oa":false,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/896e7a2f-0e00-4e0b-8771-8455859d4424/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:f04c1d6c9f584aeb8665f83ca5fb9b95","is_oa":false,"landing_page_url":"https://doaj.org/article/f04c1d6c9f584aeb8665f83ca5fb9b95","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 2, p 196 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16020196","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16020196","pdf_url":"https://www.mdpi.com/2073-8994/16/2/196/pdf?version=1707303183","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":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391614341.pdf","grobid_xml":"https://content.openalex.org/works/W4391614341.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W2016251873","https://openalex.org/W2048305092","https://openalex.org/W2570096509","https://openalex.org/W2747750973","https://openalex.org/W2886319267","https://openalex.org/W2903183953","https://openalex.org/W2921975382","https://openalex.org/W2938343470","https://openalex.org/W2967334764","https://openalex.org/W2979959870","https://openalex.org/W3037754873","https://openalex.org/W3097696962","https://openalex.org/W3118678694","https://openalex.org/W3126212142","https://openalex.org/W3136104196","https://openalex.org/W3167409357","https://openalex.org/W4200488112","https://openalex.org/W4250589301","https://openalex.org/W4281618580","https://openalex.org/W4294794097","https://openalex.org/W4296743847","https://openalex.org/W4306772919","https://openalex.org/W4317212691","https://openalex.org/W4319599449","https://openalex.org/W4360593337","https://openalex.org/W4365143177","https://openalex.org/W4366815520","https://openalex.org/W4378904335","https://openalex.org/W4380990225","https://openalex.org/W4386905837","https://openalex.org/W4387170459","https://openalex.org/W4389166469","https://openalex.org/W6753721026","https://openalex.org/W6838793428","https://openalex.org/W6852386212"],"related_works":["https://openalex.org/W4407082414","https://openalex.org/W2937491694","https://openalex.org/W2558746723","https://openalex.org/W4308131477","https://openalex.org/W3037709338","https://openalex.org/W4385473703","https://openalex.org/W4401018364","https://openalex.org/W3009899519","https://openalex.org/W2883154935","https://openalex.org/W2914542058"],"abstract_inverted_index":{"Building":[0],"upon":[1],"previous":[2],"research":[3],"in":[4,42],"conformable":[5,25,67],"fractional":[6,26,68],"calculus,":[7],"this":[8,15],"study":[9],"introduces":[10],"a":[11,18,22,95],"novel":[12,50],"identity.":[13],"Using":[14],"identity":[16],"as":[17],"foundation,":[19],"we":[20],"derive":[21],"set":[23],"of":[24,66,78,112],"Milne-type":[27],"inequalities":[28,41,72],"specifically":[29],"designed":[30],"for":[31,59],"differentiable":[32],"convex":[33,61],"functions.":[34],"The":[35,70],"obtained":[36],"results":[37],"recover":[38],"some":[39,47],"existing":[40],"the":[43,55,64,79,84,113],"literature":[44],"by":[45],"fixing":[46],"parameters.":[48],"These":[49],"contributions":[51],"aim":[52],"to":[53,101],"enrich":[54],"analytical":[56],"tools":[57],"available":[58],"studying":[60],"functions":[62],"within":[63,90],"realm":[65],"calculus.":[69],"derived":[71],"reflect":[73],"an":[74],"inherent":[75],"symmetry":[76],"characteristic":[77],"Milne":[80],"formula,":[81],"further":[82],"illustrating":[83],"balanced":[85],"and":[86,109],"harmonious":[87],"mathematical":[88],"structure":[89],"these":[91],"frameworks.":[92],"We":[93],"provide":[94],"thorough":[96],"example":[97],"with":[98],"graphical":[99],"representations":[100],"support":[102],"our":[103],"findings,":[104],"offering":[105],"both":[106],"numerical":[107],"insights":[108],"visual":[110],"confirmation":[111],"established":[114],"inequalities.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":7}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
