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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.