# Article

Ufa Mathematical Journal
Volume 13, Number 1, pp. 119-130

# Generalization Of Hadamard Type Trapezoid Inequalities For Fractional Integral Operators

Bayraktar B., Emin Özdemir M.

DOI:10.13108/2021-13-1-119

The article formulates and proves the identity with the participation of the fractional integration operator. Based on this identity, new generalized Hadamard-type integral inequalities are obtained for functions for which the second derivatives are convex and take values at intermediate points of the integration interval. These results are obtained using the convexity property of a function and two classical integral inequalities, the Hermite-Hadamard integral inequality and its other form, the power mean inequality. It is shown that the upper limit of the absolute error of inequality decreases in approximately $n^{2}$ times, where $n$ is the number of intermediate points. In a particular case, the obtained estimates are consistent with known estimates in the literature. The results obtained in the article can be used in further researches in the integro-differential fractional calculus.