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.

Convex analysis and mathematical inequalities are now essential to the development of numerous pure and applied scientific domains. In this article, first we introduce the concept of n-fractional polynomial s-like m-preinvex function. In addition, we introduce, the new variant of Hermite-Hadamard type inequality via newly introduced concept pertaining to the k-fractional operator. Furthermore, we demonstrate the applications to matrix and bivariat analysis via newly introduce Hermite-Hadamard type inequality. The study’s conclusions present unique perspectives and contributions to the field, offering fresh and noteworthy improvements over previous research.