# Hermite–Hadamard-type inequalities arising from tempered fractional integrals including twice-differentiable functions

### Abstract

UDC 517.5

We propose a new method for the investigation of integral identities according to tempered fractional operators. In addition, we prove the midpoint-type and trapezoid-type inequalities by using twice-differentiable convex functions associated with tempered fractional integral operators. We use the well-known Hölder inequality and the power-mean inequality in order to obtain inequalities of these types. The resulting Hermite–Hadamard-type inequalities are generalizations of some investigations in this field, involving Riemann–Liouville fractional integrals.

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*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 76, no. 9, Sept. 2024, pp. 1395 -11, doi:10.3842/umzh.v76i9.7640.

Copyright (c) 2024 fatih HEZENCİ, Huseyin Budak, Muhammad Amer Latif

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