{"id":"https://openalex.org/W7036780455","doi":null,"title":"A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators","display_name":"A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators","publication_year":2025,"publication_date":"2025-03-01","ids":{"openalex":"https://openalex.org/W7036780455"},"language":"en","primary_location":{"id":"pmh:oai:doaj.org/article:64b826efaea44349afdc78666453b577","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/64b826efaea44349afdc78666453b577","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,"listed_in":[],"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":"Surveys in Mathematics and its Applications, Vol 20 (2025), Pp 25-74 (2025)","raw_type":"article"},"volume":null,"type":"article","indexed_in":["doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/64b826efaea44349afdc78666453b577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Muhammad Tariq","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I180291457","display_name":"Mehran University of Engineering and Technology","ror":"https://ror.org/0575ttm03","country_code":"PK","type":"education","lineage":["https://openalex.org/I180291457"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Tariq","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan","institution_ids":["https://openalex.org/I180291457"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5154263595","display_name":"Asif Ali Shaikh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I180291457","display_name":"Mehran University of Engineering and Technology","ror":"https://ror.org/0575ttm03","country_code":"PK","type":"education","lineage":["https://openalex.org/I180291457"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Asif Ali Shaikh","raw_affiliation_strings":["Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan","institution_ids":["https://openalex.org/I180291457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079917613","display_name":"SOTIRIS K. NTOUYAS","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Sotiris K. Ntouyas","raw_affiliation_strings":["Department of mathematics, University of Ioannina, 451 10 Ioannina, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of mathematics, University of Ioannina, 451 10 Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.45348347,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"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":1.0,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.0,"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/fractional-integral-operators","display_name":"fractional integral operators","score":0.9940000176429749},{"id":"https://openalex.org/keywords/convex-functions","display_name":"convex functions","score":0.8870000243186951},{"id":"https://openalex.org/keywords/h-convex-functions","display_name":"h-convex functions","score":0.8970000147819519},{"id":"https://openalex.org/keywords/m-convex-functions","display_name":"m-convex functions","score":0.8550000190734863},{"id":"https://openalex.org/keywords/s-convex-functions","display_name":"s-convex functions","score":0.925000011920929},{"id":"https://openalex.org/keywords/interval-valued-functions","display_name":"interval-valued functions","score":0.7910000085830688},{"id":"https://openalex.org/keywords/preinvex-functions","display_name":"preinvex functions","score":0.8799999952316284},{"id":"https://openalex.org/keywords/riemann-liouville-fractional-integral","display_name":"Riemann-Liouville fractional integral","score":0.9279999732971191},{"id":"https://openalex.org/keywords/katugampola-fractional-integral","display_name":"Katugampola fractional integral","score":0.9700000286102295},{"id":"https://openalex.org/keywords/conformable-fractional-integrals","display_name":"conformable fractional integrals","score":0.9539999961853027},{"id":"https://openalex.org/keywords/atangana-baleanu-fractional-integral","display_name":"Atangana-Baleanu fractional integral","score":0.9229999780654907},{"id":"https://openalex.org/keywords/generalized-fractional-integrals","display_name":"generalized fractional integrals","score":0.878000020980835},{"id":"https://openalex.org/keywords/exponential-kernel","display_name":"exponential kernel","score":0.7400000095367432}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7717999815940857},{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.7692000269889832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7330999970436096},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5317000150680542},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.48489999771118164},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46000000834465027},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4544000029563904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4490000009536743},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.39660000801086426},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C53819440","wikidata":"https://www.wikidata.org/wiki/Q1419948","display_name":"Exponential integral","level":4,"score":0.3165999948978424},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:doaj.org/article:64b826efaea44349afdc78666453b577","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/64b826efaea44349afdc78666453b577","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,"listed_in":[],"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":"Surveys in Mathematics and its Applications, Vol 20 (2025), Pp 25-74 (2025)","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:64b826efaea44349afdc78666453b577","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/64b826efaea44349afdc78666453b577","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,"listed_in":[],"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":"Surveys in Mathematics and its Applications, Vol 20 (2025), Pp 25-74 (2025)","raw_type":"article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Reduced inequalities","score":0.41653093695640564,"id":"https://metadata.un.org/sdg/10"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"the":[1,6,95],"frame":[2],"of":[3,27,39,41,76,78,115],"fractional":[4,45,96,101,104,107,110,112,119,122,125,128,132,135,139],"calculus,":[5],"term":[7],"convexity":[8],"is":[9,31],"primarily":[10],"utilized":[11],"to":[12,32,44],"address":[13],"several":[14],"challenges":[15],"in":[16,94],"both":[17],"pure":[18],"and":[19,25,70,90,137],"applied":[20],"research.":[21],"The":[22],"main":[23],"focus":[24],"objective":[26],"this":[28],"review":[29],"paper":[30],"present":[33],"Pachpatte-type":[34],"inequalities":[35],"involving":[36],"a":[37,74],"variety":[38,75],"classes":[40,77],"convexities":[42],"pertaining":[43],"integral":[46,97,113,136,140],"operators,":[47],"such":[48,83],"as":[49,84],"h-convex,":[50,54,59],"m-convex,":[51],"s-convex,":[52],"interval":[53,57],"harmonically":[55,58,64],"convex,":[56,66],"LR-convex":[60],"interval-valued,":[61],"cr-\\mathsfh-convex,":[62],"n-polynomial":[63,88],"s-type":[65],"\u2111s-convex,":[67],"(\u03b1,m)-convex,":[68],"p-convex":[69],"(p,h)-convex":[71],"functions.":[72,92],"Moreover":[73],"preinvex":[79,89],"functions":[80],"are":[81,99],"included,":[82],"(s,m,\u03be)-preinvex,":[85],"cr-\\mathsfh-preinvex,":[86],"m-preinvex,":[87],"interval-valued":[91],"Included":[93],"operators":[98],"Riemann--Liouville":[100],"integral,":[102,105,108,111,120,123,126,129,133],"k-Riemann--Liouville":[103],"(k-r)-Riemann--Liouville":[106],"\u03a8-Riemann--Liouville":[109],"operator":[114],"exponential":[116],"kernel,":[117],"generalized":[118],"Caputo-Fabrizio":[121],"Katugampola":[124],"conformable":[127,131],"genera-lized":[130],"non-conformable":[134],"Atangana-Baleanu":[138],"operator.":[141]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}