Generalized integral inequalities for ABK-fractional integral operators

Abstract

In this paper, we employ new version of the Atangana-Baleanu integral operator namely ABK-fractional integrals to obtain two general integral identities complying second-order derivatives for a given function. Thus allowing us to derive new generalized Hermite-Hadamard type inequalities via ABK- fractional integrals. Moreover we give several new versions of Mid-point and Trapezoid type inequalities by employing Hölder, Young and Jensen inequalities.

Keywords

• differentiable convex functions
• hölder inequality
• young inequality
• power mean inequality
• katugampola fractional integral
• ab-fractional integral
• abk-fractional integral