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 �-Riemann�Liouville fractional integral operators. They generalize, complement and extend existing results in the literature. By taking m � 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. © 2021 the Author(s), licensee AIMS Press.