New Hadamard–Mercer Inequalities Pertaining Atangana–Baleanu Operator in Katugampola Sense with Applications

We formulate Hermite–Hadamard–Mercer type inequalities for (AB_K -FI) (Atangana–Baleanu Katagampula Fractional Integral) operators. We present new Dragomir–Agarwal type identities and establish a variants of Jensen–Hermite–Hadamard type inequalities involving AB_K -FI operators for differentiable convex mappings. We present new bounds by employing Young and Hölder inequalities. We make links between our findings and a number of well-known discoveries in the literature. Finally, to support the effectiveness of our obtain results, we expose some inequalities examples in terms of Modified Bessel functions and matrices. The findings of this paper may lead to more research in this field.