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Research Article | Open Access

Hadamard and Fejér-Hadamard inequalities for generalized k-fractional integrals involving further extension of Mittag-Leffler function

Ye Yue1, Ghulam Farid2, Ayșe Kübra Demirel3, Waqas Nazeer4, Yinghui Zhao1( )
School of Science, Shijiazhuang University, Shijiazhuang 050035, China
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
Department of Mathematics, Ordu University, Ordu, Turkey
Department of Mathematics, Government College University, Lahore, Pakistan
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Abstract

In this paper, k-fractional integral operators containing further extension of Mittag-Leffler function are defined firstly. Then, the first and second version of Hadamard and Fejér-Hadamard inequalities for generalized k-fractional integrals are obtained. Finally, by using these generalized k-fractional integrals containing Mittag-Leffler functions, results for p-convex functions are obtained. The results for convex functions can be deduced by taking p = 1.

Keywords

Hadamard inequalityFejér-Hadamard inequalityconvex functionp-convex functionk-fractional integralsMittag-Leffler function
CLC number: 26A51, 26A33, 33E12, 26D15, 26A51, 26B25

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 681-703
DOI: 10.3934/math.2022043

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Yue Y, Farid G, Demirel AK, et al. Hadamard and Fejér-Hadamard inequalities for generalized k-fractional integrals involving further extension of Mittag-Leffler function. AIMS Mathematics, 2022, 7(1): 681-703. https://doi.org/10.3934/math.2022043

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Received: 06 July 2021
Accepted: 30 August 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)