{"id":"https://openalex.org/W4319598512","doi":"https://doi.org/10.3390/sym15020451","title":"Fractional Multiplicative Bullen-Type Inequalities for Multiplicative Differentiable Functions","display_name":"Fractional Multiplicative Bullen-Type Inequalities for Multiplicative Differentiable Functions","publication_year":2023,"publication_date":"2023-02-08","ids":{"openalex":"https://openalex.org/W4319598512","doi":"https://doi.org/10.3390/sym15020451"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020451","pdf_url":"https://www.mdpi.com/2073-8994/15/2/451/pdf?version=1675844620","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/2073-8994/15/2/451/pdf?version=1675844620","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041958112","display_name":"Hamid Boulares","orcid":"https://orcid.org/0000-0001-9994-0534"},"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":"Hamid Boulares","raw_affiliation_strings":["Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","Laboratory of Analysis and Control of Differential Equations \"ACED\", Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]},{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \"ACED\", Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]}]},{"author_position":"middle","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, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","Laboratory of Analysis and Control of Differential Equations \"ACED\", Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]},{"raw_affiliation_string":"Laboratory of Analysis and Control of Differential Equations \"ACED\", Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria","institution_ids":["https://openalex.org/I4210097536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013003394","display_name":"Abdelkader Moumen","orcid":"https://orcid.org/0000-0003-1080-3686"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Abdelkader Moumen","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1080-3686","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016185347","display_name":"Ramsha Shafqat","orcid":"https://orcid.org/0000-0002-3610-339X"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"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":"Ramsha Shafqat","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3610-339X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435","https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000154542","display_name":"Hicham Saber","orcid":"https://orcid.org/0000-0003-3453-9277"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hicham Saber","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013716670","display_name":"Tariq Alraqad","orcid":"https://orcid.org/0000-0002-8881-4812"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tariq Alraqad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007779636","display_name":"Ekram E. Ali","orcid":"https://orcid.org/0000-0002-5477-0065"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ekram E. Ali","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5477-0065","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 55425, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5013003394"],"corresponding_institution_ids":["https://openalex.org/I4210088963"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":19.0866,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.99869786,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"15","issue":"2","first_page":"451","last_page":"451"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9882000088691711,"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":0.9751999974250793,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8561053276062012},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.8249412775039673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.736746609210968},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.47535914182662964},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4724569618701935},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.44586291909217834},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4349508583545685},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3944843113422394},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38143014907836914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24351012706756592},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04685327410697937}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8561053276062012},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8249412775039673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.736746609210968},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.47535914182662964},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4724569618701935},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.44586291909217834},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4349508583545685},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3944843113422394},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38143014907836914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24351012706756592},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04685327410697937},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020451","pdf_url":"https://www.mdpi.com/2073-8994/15/2/451/pdf?version=1675844620","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:733287df124e4e70804cf2f882095da5","is_oa":false,"landing_page_url":"https://doaj.org/article/733287df124e4e70804cf2f882095da5","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 15, Iss 2, p 451 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/451/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020451","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/sym15020451","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15020451","pdf_url":"https://www.mdpi.com/2073-8994/15/2/451/pdf?version=1675844620","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":0.6800000071525574,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4319598512.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W165585849","https://openalex.org/W181947251","https://openalex.org/W1625618885","https://openalex.org/W1964092742","https://openalex.org/W1978037192","https://openalex.org/W2022456747","https://openalex.org/W2032927390","https://openalex.org/W2056135743","https://openalex.org/W2102808049","https://openalex.org/W2106002651","https://openalex.org/W2151162372","https://openalex.org/W2304758964","https://openalex.org/W2736824113","https://openalex.org/W2917597246","https://openalex.org/W2962760085","https://openalex.org/W2965312062","https://openalex.org/W2972125909","https://openalex.org/W2992224883","https://openalex.org/W3000209180","https://openalex.org/W3041710384","https://openalex.org/W3045610251","https://openalex.org/W3114933723","https://openalex.org/W3128613614","https://openalex.org/W3135016370","https://openalex.org/W3161184056","https://openalex.org/W4200096789","https://openalex.org/W4238430941","https://openalex.org/W6698366594","https://openalex.org/W6740935021","https://openalex.org/W6770813897","https://openalex.org/W6791541759","https://openalex.org/W7010238735"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W4318195686","https://openalex.org/W4251867247","https://openalex.org/W2975999359","https://openalex.org/W2914542058","https://openalex.org/W4385382439","https://openalex.org/W4387635768"],"abstract_inverted_index":{"Various":[0],"scholars":[1],"have":[2],"lately":[3],"employed":[4],"a":[5,24],"wide":[6],"range":[7],"of":[8,14,51],"strategies":[9],"to":[10],"resolve":[11],"specific":[12],"types":[13],"symmetrical":[15],"fractional":[16,26,40],"differential":[17],"equations.":[18],"In":[19],"this":[20,34],"paper,":[21],"we":[22,36],"propose":[23],"new":[25,39],"identity":[27],"for":[28,44],"multiplicatively":[29],"differentiable":[30,46],"functions;":[31],"based":[32],"on":[33],"identity,":[35],"establish":[37],"some":[38],"multiplicative":[41,45],"Bullen-type":[42],"inequalities":[43],"convex":[47],"functions.":[48],"Some":[49],"applications":[50],"the":[52],"obtained":[53],"results":[54],"are":[55],"given.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}