HERMITE–HADAMARD-TYPE INEQUALITIES INVOLVING SEVERAL KINDS OF FRACTIONAL CALCULUS FOR HARMONICALLY CONVEX FUNCTIONS

Wenbing Sun and Haiyang Wan
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Wenbing Sun: School of Science, Shaoyang University, Shaoyang 422000, P. R. China
Haiyang Wan: School of Science, Shaoyang University, Shaoyang 422000, P. R. China†Department of Mathematics and Theories Peng Cheng Laboratory, Shenzhen, Guangdong 518000, P. R. China‡Future tech, South China University of Technology, Guangzhou 510640, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-16

Abstract: In this paper, we use the properties of Atangana–Baleanu (AB) fractional calculus and Prabhakar fractional calculus to construct some novel Hermite–Hadamard-type fractional integral inequalities for harmonically convex functions. And these inequalities are represented by the Mittag-Leffler functions. Finally, several special inequalities are established to illustrate the applications of our conclusions in special means.

Keywords: Atangana–Baleanu Fractional Calculus; Prabhakar Fractional Integrals; Hermite–Hadamard-type Inequalities; Harmonically Convex Function; Mittag-Leffler Function (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501098

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