Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2209 |
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| author | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong |
| author_facet | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong |
| author_sort | Soubhagya Kumar Sahoo |
| collection | DOAJ |
| description | The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the <i>k</i>-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how <b>q</b>-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role. |
| first_indexed | 2024-03-10T05:01:34Z |
| format | Article |
| id | doaj.art-d9abdd6353064fe0a1feea967f9b8f6a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:01:34Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d9abdd6353064fe0a1feea967f9b8f6a2023-11-23T01:47:01ZengMDPI AGSymmetry2073-89942021-11-011311220910.3390/sym13112209Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable MappingsSoubhagya Kumar Sahoo0Muhammad Tariq1Hijaz Ahmad2Ayman A. Aly3Bassem F. Felemban4Phatiphat Thounthong5Department of Mathematics, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, IndiaDepartment of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, PakistanDepartment of Computer Engineering, Biruni University, Istanbul 34025, TurkeyDepartment of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mechanical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaRenewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandThe theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the <i>k</i>-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how <b>q</b>-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.https://www.mdpi.com/2073-8994/13/11/2209convex functionHermite-Hadamard inequalityh-convex functionRiemann-Liouville <i>k</i>-fractional integrals |
| spellingShingle | Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings Symmetry convex function Hermite-Hadamard inequality h-convex function Riemann-Liouville <i>k</i>-fractional integrals |
| title | Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings |
| title_full | Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings |
| title_fullStr | Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings |
| title_full_unstemmed | Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings |
| title_short | Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings |
| title_sort | some hermite hadamard type fractional integral inequalities involving twice differentiable mappings |
| topic | convex function Hermite-Hadamard inequality h-convex function Riemann-Liouville <i>k</i>-fractional integrals |
| url | https://www.mdpi.com/2073-8994/13/11/2209 |
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