Some integral inequalities via Caputo and Liouville fractional integral operators for m-convex functions

TL;DR

This paper develops new integral inequalities involving Caputo and Liouville fractional operators for m-convex functions, providing bounds that extend existing mathematical inequalities in fractional calculus.

Contribution

It introduces novel inequalities for Caputo fractional derivatives specifically tailored for m-convex functions, expanding the theoretical framework of fractional integral inequalities.

Findings

Derived new inequalities for Caputo fractional derivatives

Established bounds for m-convex functions using fractional calculus

Extended existing inequalities in fractional calculus literature

Abstract

This short study consists of two parts, firstly we obtain some inequalities on Caputo Fractional derivatives using the elementary inequalities. Secondly we establish several new inequalities including Caputo fractional derivatives for m-convex functions. In general, in this work we obtain upper bounds for the left sides of Lemma 1[10] and lemma 2[20].