Fractional inequalities of the Hermite–Hadamard type for $ m $-polynomial convex and harmonically convex functions

Abstract

In this paper, it is our purpose to establish some new fractional inequalities of the Hermite–Hadamard type for the $ m $-polynomial convex and harmonically convex functions. Our results involve the Caputo–Fabrizio and $  \zeta $-Riemann–Liouville fractional integral operators. They generalize, complement and extend existing results in the literature. By taking $ m\geq 2 $, we deduce loads of new and interesting inequalities. We expect that the thought laid out in this work will provoke advance examinations in this course.

Keywords

• hermite–hadamard
• m-polynomial convex
• m-polynomial harmonically convex
• riemann–liouville
• caputo–fabrizio