Novel Fractional Hermite–Hadamard and Product-Type Inequalities via Raina Function and Preinvex Mappings with Entropy Applications

In this paper, we employ the Atangana-Baleanu fractional integral operator to develop new versions of Hermite–Hadamard and Pachpatte-type integral inequalities within the framework of generalized convexity involving Raina’s function. By this approach, we derive a novel fractional integral identity associated with Raina’s functions. Furthermore, leveraging Young’s inequality, the power mean inequality, and Hölder’s inequality, we establish several new extensions of Hermite–Hadamard-type inequalities via the Atangana–Baleanu fractional operator. Our results significantly improve upon existing findings, both in terms of generality and special cases. To validate our results, we provide remarks that recover various earlier inequalities. Additionally, we present applications related to entropy measures that demonstrate the practical utility of our main findings.