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Hermite–Hadamard-Type Inequalities Involving Several Kinds Of Fractional Calculus For Harmonically Convex Functions

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wenbing Sun & Haiyang Wan, 2023. "Hermite–Hadamard-Type Inequalities Involving Several Kinds Of Fractional Calculus For Harmonically Convex Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:09:n:s0218348x23501098
    DOI: 10.1142/S0218348X23501098
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    Cited by:

    1. Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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