In this paper, we establish new inequalities of the Hermite–Hadamard, midpoint and trapezoid types for functions whose first derivatives in absolute value are η-quasiconvex by means of generalized fractional integral operators with respect to another function ω : [α, β] → (0,∞). Our theorems reduce to results involving the Riemann–Liouville fractional integral operators if ω is the identity map, and results involving the Hadamard operators if ω(x) = ln x. More inequalities can be deduced by choosing different bifunctions for η. To the best of our knowledge, the results obtained herein are new and we hope that they will stimulate further interest in this direction.