On inequalities of Hermite-Hadamard-Mercer type involving Riemann-Liouville fractional integrals

Thabet Abdeljawad; Muhammad Aamir Ali; Pshtiwan Othman Mohammed; Artion Kashuri; Thabet Abdeljawad; Muhammad Aamir Ali; Pshtiwan Othman Mohammed; Artion Kashuri

doi:10.3934/math.2021043

AIMS Mathematics

2021, Volume 6, Issue 1: 712-725. doi: 10.3934/math.2021043

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Research article

On inequalities of Hermite-Hadamard-Mercer type involving Riemann-Liouville fractional integrals

1.
Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
2.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
3.
Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan
4.
Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, China
5.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
6.
Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania

Received: 04 July 2020 Accepted: 21 October 2020 Published: 28 October 2020
MSC : 26D07, 26D10, 26D15

The goal of this article is to establish many inequalities of Hermite-Hadamard-Mercer type involving Riemann-Liouville fractional operators. We also establish some related fractional integral inequalities connected to the left side of Hermite-Hadamard-Mercer type inequality for differentiable convex functions. Further remarks and observations for these results are given. Finally, we see the efficiency of our inequalities via some applications on special means.
- Riemann-Liouville fractional integral,
- Hermite-Hadamard-Mercer inequality,
- Jensen-Mercer inequality
Citation: Thabet Abdeljawad, Muhammad Aamir Ali, Pshtiwan Othman Mohammed, Artion Kashuri. On inequalities of Hermite-Hadamard-Mercer type involving Riemann-Liouville fractional integrals[J]. AIMS Mathematics, 2021, 6(1): 712-725. doi: 10.3934/math.2021043

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Abstract

The goal of this article is to establish many inequalities of Hermite-Hadamard-Mercer type involving Riemann-Liouville fractional operators. We also establish some related fractional integral inequalities connected to the left side of Hermite-Hadamard-Mercer type inequality for differentiable convex functions. Further remarks and observations for these results are given. Finally, we see the efficiency of our inequalities via some applications on special means.

References

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