(<i>k</i>, <i>ψ</i>)-Proportional Fractional Integral Pólya–Szegö- and Grüss-Type Inequalities

Abstract

The purpose of this research was to discover a novel method to recover k-fractional integral inequalities of the Pólya–Szegö-type. We employ these generalized inequalities to investigate some new fractional integral inequalities of the Grüss-type. More precisely, we generalize the proportional fractional operators with respect to another strictly increasing continuous function ψ. Then, we state and prove some of its properties and special cases. With the help of this generalized operator, we investigate some Pólya–Szegö- and Grüss-type fractional integral inequalities. The functions used in this work are bounded by two positive functions to obtain Pólya–Szegö- and Grüss-type k-fractional integral inequalities in a new sense. Moreover, we discuss some new special cases of the Pólya–Szegö- and Grüss-type inequalities through this work.

Keywords

• Pólya–Szegö inequalities
• Grüss inequalities
• fractional inequalities
• <i>ψ</i>-proportional fractional operators