On New Generalized Fractional Integral Operators and Related Fractional Inequalities

Year 2020, Volume: 8 Issue: 2, 268 - 278, 27.10.2020

Tuba Tunç , Hüseyin Budak , Fuat Usta , Mehmet Zeki Sarıkaya

Abstract

In this paper, we define the generalized $k$-fractional integrals of a function with respect to the another function which generalizes many different types of fractional integrals such as Riemann-Liouville fractional, Hadamard fractional integrals, Katugampola fractional integral, $(k,s)$-fractional integral operators. Moreover, we obtain Hermite-Hadamard inequalities utilizing $k$-fractional integrals of a function with respect to the another function. We also investigate trapezoid inequalities for the functions whose derivatives in absolute value are convex. Finally, some special cases of these inequalities are given.

Keywords

Fractional integral operators, Hermite-Hadamard inequality, midpoint inequality, convex function.

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