New Versions of the Hermite--Hadamard Inequality in the Framework of Weighted Riemann--Liouville Integrals

This paper presents new Hermite–Hadamard type inequalities within a unified analytic framework. The study uses the modified (h,m)-class of convex functions, which consolidates different notions of convexity. By applying weighted Riemann–Liouville operators, a flexible scheme is developed to control inequality behavior through weight functions and model parameters. The results recover classical and recent inequalities under suitable choices and demonstrate practical relevance with exponential weights, enabling direct applications to fractional integrals and complex mathematical models.