On Chebyshev type Inequalities using Generalized k-Fractional Integral Operator

TL;DR

This paper introduces new inequalities involving a generalized k-fractional integral operator based on the Gauss hypergeometric function, extending Chebyshev inequalities for synchronous functions.

Contribution

It develops novel generalized k-fractional integral inequalities using the extended Chebyshev functional, expanding the theoretical framework of fractional calculus.

Findings

New inequalities for generalized k-fractional integrals established

Extended Chebyshev functional applied to synchronous functions

Results contribute to fractional calculus and inequality theory

Abstract

In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on generalized k-fractional integral inequalities by considering the extended Chebyshev functional in case of synchronous function and some other inequalities.