Some Novel Fractional Integral Inequalities for m-Convex and (α,m)-Convex Functions

Year 2025, Volume: 11 Issue: 1-2, 1 - 8, 29.12.2025

Sinan Aslan , Ahmet Ocak Akdemir

Abstract

In this study, several novel integral inequalities are established for various classes of convex functions by employing the Caputo–Fabrizio fractional integral operator. Specifically, new inequalities are derived for m-convex and (α,m)-convex functions. The presented results generalize and extend existing inequalities in the literature, reducing to known outcomes for certain specific parameter values. The derivations rely on the fundamental properties of the Caputo–Fabrizio fractional operator, formal definitions of different types of convexity, and standard analytical techniques.

Keywords

Caputo-Fabrizio fractional integral operator , m-convex functions , (Alpha,m)- convex functions

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