Hermite-Hadamard-Fejer type inequalities via fractional integral of a function concerning another function

Dumitru Baleanu; Muhammad Samraiz; Zahida Perveen; Sajid Iqbal; Kottakkaran Sooppy Nisar; Gauhar Rahman; Dumitru Baleanu; Muhammad Samraiz; Zahida Perveen; Sajid Iqbal; Kottakkaran Sooppy Nisar; Gauhar Rahman

doi:10.3934/math.2021253

AIMS Mathematics

2021, Volume 6, Issue 5: 4280-4295. doi: 10.3934/math.2021253

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Research article

Hermite-Hadamard-Fejer type inequalities via fractional integral of a function concerning another function

1.
Department of Mathematics, Cankaya University, 06530 Ankara, Turkey
2.
Institute of Space Sciences, 077125 Magurele, Romania
3.
Department of Medical Research, China Medical University Hospital, China Medical University, 40250 Taichung, Taiwan
4.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
5.
Department of Mathematics, Riphah International University, Faisalabad Campus, Satyana Road, 38000 Faisalabad, Pakistan
6.
Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, 11991 Wadi Aldawaser, Saudi Arabia
7.
5-Department of Mathematics and Statistics, Hazara University Mansehra, Pakistan

Received: 31 October 2020 Accepted: 18 January 2021 Published: 07 February 2021
MSC : 26D15, 26A33, 26A51, 26D07, 26D10

In this paper, we at first develop a generalized integral identity by associating Riemann-Liouville (RL) fractional integral of a function concerning another function. By using this identity estimates for various convexities are accomplish which are fractional integral inequalities. From our results, we obtained bounds of known fractional results which are discussed in detail. As applications of the derived results, we obtain the mid-point-type inequalities. These outcomes might be helpful in the investigation of the uniqueness of partial differential equations and fractional boundary value problems.
- Hermite-Hadamard-Fejer inequalities,
- convex function,
- generalized fractional integral,
- mid-point inequality,
- Riemann-Liouville
Citation: Dumitru Baleanu, Muhammad Samraiz, Zahida Perveen, Sajid Iqbal, Kottakkaran Sooppy Nisar, Gauhar Rahman. Hermite-Hadamard-Fejer type inequalities via fractional integral of a function concerning another function[J]. AIMS Mathematics, 2021, 6(5): 4280-4295. doi: 10.3934/math.2021253

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Abstract

In this paper, we at first develop a generalized integral identity by associating Riemann-Liouville (RL) fractional integral of a function concerning another function. By using this identity estimates for various convexities are accomplish which are fractional integral inequalities. From our results, we obtained bounds of known fractional results which are discussed in detail. As applications of the derived results, we obtain the mid-point-type inequalities. These outcomes might be helpful in the investigation of the uniqueness of partial differential equations and fractional boundary value problems.

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