Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means
Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/602 |
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| author | Bibhakar Kodamasingh Soubhagya Kumar Sahoo Wajid Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas Muhammad Tariq |
| author_facet | Bibhakar Kodamasingh Soubhagya Kumar Sahoo Wajid Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas Muhammad Tariq |
| author_sort | Bibhakar Kodamasingh |
| collection | DOAJ |
| description | Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers. |
| first_indexed | 2024-03-09T19:15:50Z |
| format | Article |
| id | doaj.art-156d34d69ca541799934e838e2996b6f |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:15:50Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-156d34d69ca541799934e838e2996b6f2023-11-24T03:44:07ZengMDPI AGAxioms2075-16802022-10-01111160210.3390/axioms11110602Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special MeansBibhakar Kodamasingh0Soubhagya Kumar Sahoo1Wajid Ali Shaikh2Kamsing Nonlaopon3Sotiris K. Ntouyas4Muhammad Tariq5Department of Mathematics, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Mathematics, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Mathematics and Statistics, Quest, Nawabshah 67450, PakistanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanFractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers.https://www.mdpi.com/2075-1680/11/11/602Hermite–Hadamard inequalityrefined exponential convex functionhypergeometric functionpower mean inequalityfractional integral operatorprobability density function |
| spellingShingle | Bibhakar Kodamasingh Soubhagya Kumar Sahoo Wajid Ali Shaikh Kamsing Nonlaopon Sotiris K. Ntouyas Muhammad Tariq Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means Axioms Hermite–Hadamard inequality refined exponential convex function hypergeometric function power mean inequality fractional integral operator probability density function |
| title | Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means |
| title_full | Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means |
| title_fullStr | Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means |
| title_full_unstemmed | Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means |
| title_short | Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means |
| title_sort | some new integral inequalities involving fractional operator with applications to probability density functions and special means |
| topic | Hermite–Hadamard inequality refined exponential convex function hypergeometric function power mean inequality fractional integral operator probability density function |
| url | https://www.mdpi.com/2075-1680/11/11/602 |
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