HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS

Shu-Hong Wang; Xu-Ran Hai

doi:10.11948/20210033

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 1650-1667

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Shu-Hong Wang, Xu-Ran Hai. HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1650-1667. doi: 10.11948/20210033

Citation:

Shu-Hong Wang, Xu-Ran Hai. HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1650-1667. doi: 10.11948/20210033

HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS

Shu-Hong Wang^1, ,,
Xu-Ran Hai^1,

1.
College of Mathematics and Physics, Inner Mongolia Minzu University, Ximen Street, 028000 Tongliao, China

Author Bio: Email: 2651721297@qq.com(X. R. Hai)
Corresponding author: Email: shuhong7682@163.com(S. H. Wang)
Fund Project: The authors were supported by the PhD Research Foundation of Inner Mongolia Minzu University (No. BS402) and by Basic Scientific Research Professional Foundation of Universities Affiliated to Inner Mongolia Autonomous Region (GXKY22159)

Abstract

Abstract

In the paper, basing on the Katugampola fractional integrals $ {}^\rho\mathcal{K}^\alpha_{a+}f $ and $ {}^\rho\mathcal{K}^\alpha_{b-}f $ with $ f\in\mathfrak{X}_c^p(a, b) $, the authors establish the Hermite–Hadamard type inequalities for convex functions, give their left estimates, and apply these newly-established inequalities to special means of real numbers. When $ \rho\to1 $, these results become the corresponding ones for the Riemann–Liouville fractional integrals.
- Hermite-Hadamard type inequality /
- convex function /
- special mean /
- Katugampola fractional integral
MSC: 26A33, 26D07, 26D10, 26D15

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References

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