Fractional integral operators play a vital role in establishing generalized forms of mathematical inequalities. These operators provide effective tools for modeling various scientific and engineering processes such as fracture mechanics, elasticity, heat transfer, viscoelastic deformation, and the behavior of continuous populations. In this study, we investigate a new class of Hermite–Hadamard type inequalities and verify their numerical validity. By employing a novel equality together with Hölder’s inequality, we derive several extensions of Hermite–Hadamard type inequalities through generalized convexity involving Raina’s function within the framework of fractional integral operators. Moreover, we present applications related to information divergence and entropy bounds. The results obtained here constitute significant advancements and generalizations of existing findings in the literature.