On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

Abstract

Abstract The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

Keywords

• s-convex functions
• Hermite–Hadamard inequality
• Hölder inequality
• Atangana–Baleanu integral operators
• Normalization function
• Euler gamma function