{"id":"https://openalex.org/W4407251797","doi":"https://doi.org/10.3390/computation13020046","title":"Computational Representation of Fractional Inequalities Through 2D and 3D Graphs with Applications","display_name":"Computational Representation of Fractional Inequalities Through 2D and 3D Graphs with Applications","publication_year":2025,"publication_date":"2025-02-07","ids":{"openalex":"https://openalex.org/W4407251797","doi":"https://doi.org/10.3390/computation13020046"},"language":"en","primary_location":{"id":"doi:10.3390/computation13020046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13020046","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","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/computation13020046","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060685174","display_name":"Muhammad Rizwan Younis","orcid":"https://orcid.org/0009-0004-5195-1268"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Muhammad Younis","raw_affiliation_strings":["School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012715400","display_name":"Ahsan Mehmood","orcid":"https://orcid.org/0009-0003-4729-0834"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ahsan Mehmood","raw_affiliation_strings":["School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065292084","display_name":"Muhammad Samraiz","orcid":"https://orcid.org/0000-0001-8480-2817"},"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":"Muhammad Samraiz","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052194722","display_name":"Gauhar Rahman","orcid":"https://orcid.org/0000-0002-2728-7537"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Gauhar Rahman","raw_affiliation_strings":["Department of Mathematics & Statistics, Hazara University, Mansehra 21300, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, Hazara University, Mansehra 21300, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056382866","display_name":"Salma Haque","orcid":"https://orcid.org/0000-0002-4514-0061"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Salma Haque","raw_affiliation_strings":["Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072846256","display_name":"Ahmad Aloqaily","orcid":"https://orcid.org/0000-0001-9578-2073"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad Aloqaily","raw_affiliation_strings":["Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021626938","display_name":"Nabil Mlaiki","orcid":"https://orcid.org/0000-0002-7986-886X"},"institutions":[{"id":"https://openalex.org/I142024983","display_name":"Prince Sultan University","ror":"https://ror.org/053mqrf26","country_code":"SA","type":"education","lineage":["https://openalex.org/I142024983"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nabil Mlaiki","raw_affiliation_strings":["Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia","institution_ids":["https://openalex.org/I142024983"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5060685174"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.2616,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.93057671,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"13","issue":"2","first_page":"46","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.8751999735832214,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.8751999735832214,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.8169999718666077,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.8087000250816345,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6648510694503784},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5989741683006287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4815919101238251},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36833667755126953},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3647667467594147},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28337687253952026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15281221270561218},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.10169029235839844}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6648510694503784},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5989741683006287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4815919101238251},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36833667755126953},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3647667467594147},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28337687253952026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15281221270561218},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.10169029235839844},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation13020046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13020046","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4e3e2ac3e2fd4376ab39ef5c2271fea6","is_oa":true,"landing_page_url":"https://doaj.org/article/4e3e2ac3e2fd4376ab39ef5c2271fea6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 13, Iss 2, p 46 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation13020046","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13020046","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","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/W1499073929","https://openalex.org/W1970631868","https://openalex.org/W2004032856","https://openalex.org/W2013901221","https://openalex.org/W2021308632","https://openalex.org/W2048305092","https://openalex.org/W2049888876","https://openalex.org/W2050765441","https://openalex.org/W2072789018","https://openalex.org/W2190750553","https://openalex.org/W2228681942","https://openalex.org/W2252352499","https://openalex.org/W2267484819","https://openalex.org/W2519050643","https://openalex.org/W2543430060","https://openalex.org/W2563444977","https://openalex.org/W2606953315","https://openalex.org/W2747750973","https://openalex.org/W2768544479","https://openalex.org/W2781689743","https://openalex.org/W2884996684","https://openalex.org/W2922428687","https://openalex.org/W3003330179","https://openalex.org/W3042594550","https://openalex.org/W3083867810","https://openalex.org/W3093729762","https://openalex.org/W3147623791","https://openalex.org/W4206290559","https://openalex.org/W4236165936","https://openalex.org/W4293200410","https://openalex.org/W4307703293","https://openalex.org/W4309030305","https://openalex.org/W4311505376","https://openalex.org/W4380925745","https://openalex.org/W4386841134","https://openalex.org/W6662372883","https://openalex.org/W6679519588","https://openalex.org/W6685029437","https://openalex.org/W6686907548","https://openalex.org/W6687257047","https://openalex.org/W6730176618","https://openalex.org/W6732573306","https://openalex.org/W6755947745","https://openalex.org/W6764459300"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0,119],"aim":[1],"of":[2,23],"this":[3],"research":[4,120],"article":[5],"is":[6],"to":[7,32,52,83,113],"use":[8],"the":[9,14,21,24,37,44,53,66,88,91,98],"extended":[10,62],"fractional":[11,63,134],"operators":[12,64],"involving":[13,65,133],"multivariate":[15],"Mittag\u2013Leffler":[16],"(M-M-L)":[17],"function,":[18],"we":[19,47,72,102],"provide":[20,84],"generalization":[22],"Hermite\u2013Hadamard\u2013Fejer":[25],"(H-H-F)":[26],"inequalities.":[27,100],"We":[28],"relate":[29],"these":[30],"inequalities":[31,50,106],"previously":[33],"published":[34],"disparities":[35],"in":[36,97,117],"literature":[38],"by":[39],"making":[40],"appropriate":[41],"substitutions.":[42],"In":[43],"last":[45],"section,":[46],"analyze":[48],"several":[49],"related":[51],"H-H-F":[54,99],"inequalities,":[55],"focusing":[56],"on":[57],"generalized":[58],"h-convexity":[59],"associated":[60],"with":[61,124],"M-M-L":[67],"function.":[68],"To":[69],"achieve":[70],"this,":[71],"derive":[73],"two":[74],"identities":[75],"for":[76,87,130],"locally":[77],"differentiable":[78],"functions,":[79],"which":[80],"allows":[81],"us":[82],"specific":[85,105],"estimates":[86],"differences":[89],"between":[90],"left,":[92],"middle,":[93],"and":[94,107],"right":[95],"terms":[96],"Also,":[101],"have":[103],"constructed":[104],"visualized":[108],"them":[109],"through":[110],"graphical":[111],"representations":[112],"facilitate":[114],"their":[115],"applications":[116],"analysis.":[118],"bridges":[121],"theoretical":[122],"advancements":[123],"practical":[125],"applications,":[126],"providing":[127],"high-accuracy":[128],"bounds":[129],"complex":[131],"systems":[132],"calculus.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}