Unified treatment of fractional integral inequalities via linear functionals

TL;DR

This paper develops a unified approach to fractional integral inequalities using isotonic linear functionals, providing a versatile method applicable to various fractional operators and function classes.

Contribution

It introduces a general framework for deriving inequalities involving fractional integrals through isotonic linear functionals, unifying multiple existing results.

Findings

Derived inequalities for functions with variable bounds

Established bounds for Lipschitz and Hölder functions

Unified treatment applicable to various fractional integral operators

Abstract

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals.