Hermite–Hadamard Inequalities for a New Riemann–Liouville-Type Operator

We introduce a new class of fractional remainder operators, denoted by Rα,nξ+ and Rα,nη−, which generalize and unify various classical integral identities. Using these operators, we formulate refined Hermite–Hadamard and trapezoidal inequalities for differentiable functions. The novelty of our approach lies in its symmetric kernel structure, which facilitates tighter error bounds. Numerical examples are given, including applications to non-differentiable convex functions, to demonstrate the applicability and limitations of the derived results.