{"id":"https://openalex.org/W7126079698","doi":"https://doi.org/10.58250/jnanabha.2025.55208","title":"THE GR\u00dcSS TYPE FRACTIONAL INTEGRAL INEQUALITIES OF MULTIVARIATE MITTAG-LEFFLER FUNCTION","display_name":"THE GR\u00dcSS TYPE FRACTIONAL INTEGRAL INEQUALITIES OF MULTIVARIATE MITTAG-LEFFLER FUNCTION","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W7126079698","doi":"https://doi.org/10.58250/jnanabha.2025.55208"},"language":"en","primary_location":{"id":"doi:10.58250/jnanabha.2025.55208","doi":"https://doi.org/10.58250/jnanabha.2025.55208","is_oa":true,"landing_page_url":"https://doi.org/10.58250/jnanabha.2025.55208","pdf_url":"https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_55_v2_2025/Jnanabha55%282%292025-58-66.pdf","source":{"id":"https://openalex.org/S4387285991","display_name":"jnanabha","issn_l":"0304-9892","issn":["0304-9892","2455-7463"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"jnanabha","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_55_v2_2025/Jnanabha55%282%292025-58-66.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080913083","display_name":"Meena Kumari Gurjar","orcid":"https://orcid.org/0000-0002-3821-4405","observed_orcids":["https://orcid.org/0000-0002-3821-4405"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meena Kumari Gurjar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029107868","display_name":"Preeti Chhattry","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Preeti Chhattry","raw_affiliation_strings":["Govt. Girls High School Pathariya , Mungeli , Chattisgarh , India -495113 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Govt. Girls High School Pathariya , Mungeli , Chattisgarh , India -495113 ","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092579902","display_name":"Anil Kumar Vishnoi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I178000100","display_name":"Kurukshetra University","ror":"https://ror.org/019bzvf55","country_code":"IN","type":"education","lineage":["https://openalex.org/I178000100"]},{"id":"https://openalex.org/I4724304","display_name":"Jodhpur National University","ror":"https://ror.org/03rm49h74","country_code":"IN","type":"education","lineage":["https://openalex.org/I4724304"]},{"id":"https://openalex.org/I59100879","display_name":"Jai Narain Vyas University","ror":"https://ror.org/03qnpty21","country_code":"IN","type":"education","lineage":["https://openalex.org/I59100879"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anil Kumar Vishnoi","raw_affiliation_strings":["Department of Mathematics , Kurukshetra University , Kurukshetra , India -136119 ","Department of Mathematics and Statistics , J.N.V. University , Jodhpur , Rajasthan , India- 342001 "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Kurukshetra University , Kurukshetra , India -136119 ","institution_ids":["https://openalex.org/I178000100"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , J.N.V. University , Jodhpur , Rajasthan , India- 342001 ","institution_ids":["https://openalex.org/I4724304","https://openalex.org/I59100879"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5124172025","display_name":"Rajneesh Kumar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajneesh Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"02","first_page":"58","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"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/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":0.0,"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/gruss-type-inequalities","display_name":"Gr\u00fcss type inequalities","score":0.8600000143051147},{"id":"https://openalex.org/keywords/fractional-integral-inequalities","display_name":"fractional integral inequalities","score":0.8529999852180481},{"id":"https://openalex.org/keywords/riemann-liouville-integral","display_name":"Riemann-Liouville integral","score":0.9480000138282776},{"id":"https://openalex.org/keywords/generalized-fractional-integrals","display_name":"generalized fractional integrals","score":0.8610000014305115},{"id":"https://openalex.org/keywords/fractional-integral-operators","display_name":"fractional integral operators","score":0.6420000195503235}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7623999714851379},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6600000262260437},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5952000021934509},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5139999985694885},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4708999991416931},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.319599986076355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31150001287460327},{"id":"https://openalex.org/C99336924","wikidata":"https://www.wikidata.org/wiki/Q598146","display_name":"Surface integral","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C38180746","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate analysis","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C54865166","wikidata":"https://www.wikidata.org/wiki/Q844937","display_name":"Multiple integral","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.27140000462532043},{"id":"https://openalex.org/C118871108","wikidata":"https://www.wikidata.org/wiki/Q1750507","display_name":"Beta function (physics)","level":5,"score":0.27000001072883606},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C75023562","wikidata":"https://www.wikidata.org/wiki/Q467699","display_name":"Line integral","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C37608338","wikidata":"https://www.wikidata.org/wiki/Q510733","display_name":"Gronwall's inequality","level":3,"score":0.25999999046325684}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.58250/jnanabha.2025.55208","doi":"https://doi.org/10.58250/jnanabha.2025.55208","is_oa":true,"landing_page_url":"https://doi.org/10.58250/jnanabha.2025.55208","pdf_url":"https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_55_v2_2025/Jnanabha55%282%292025-58-66.pdf","source":{"id":"https://openalex.org/S4387285991","display_name":"jnanabha","issn_l":"0304-9892","issn":["0304-9892","2455-7463"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"jnanabha","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.58250/jnanabha.2025.55208","doi":"https://doi.org/10.58250/jnanabha.2025.55208","is_oa":true,"landing_page_url":"https://doi.org/10.58250/jnanabha.2025.55208","pdf_url":"https://docs.vijnanaparishadofindia.org/jnanabha/jnanabha_volume_55_v2_2025/Jnanabha55%282%292025-58-66.pdf","source":{"id":"https://openalex.org/S4387285991","display_name":"jnanabha","issn_l":"0304-9892","issn":["0304-9892","2455-7463"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"jnanabha","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7126079698.pdf","grobid_xml":"https://content.openalex.org/works/W7126079698.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4297348226","https://openalex.org/W2954522399","https://openalex.org/W4220880823","https://openalex.org/W7171960268","https://openalex.org/W4404692637","https://openalex.org/W4295717995","https://openalex.org/W4389299436","https://openalex.org/W2322963367","https://openalex.org/W3124514993","https://openalex.org/W4245929790"],"abstract_inverted_index":{"Integral":[0],"inequalities":[1,18,31],"are":[2,8,67],"becoming":[3],"more":[4],"popular":[5],"because":[6],"they":[7],"useful":[9],"in":[10],"many":[11],"areas.":[12],"The":[13],"researchers":[14],"have":[15],"studied":[16],"integral":[17,30,44,66],"using":[19],"various":[20],"methods.":[21],"In":[22],"this":[23],"paper,":[24],"we":[25],"want":[26],"to":[27,69],"create":[28],"new":[29],"such":[32],"as":[33],"Gr\u00a8uss":[34],"type":[35],"inequalities,":[36],"and":[37,62],"other":[38],"similar":[39],"ones,":[40],"for":[41],"the":[42,48,56,59,63],"fractional":[43,65],"operator":[45],"that":[46],"uses":[47],"multivariate":[49],"Mittag-Leffler":[50],"function.":[51],"We":[52,73],"look":[53],"at":[54],"how":[55],"Riemann-Liouville":[57],"integral,":[58,61],"Prabhakar":[60],"generalized":[64],"related":[68],"make":[70],"specific":[71],"conclusions.":[72],"support":[74],"our":[75],"findings":[76],"by":[77],"giving":[78],"additional":[79],"details.":[80]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-01-30T00:00:00"}
