Midpoint‐Type Inequalities for a Class of Fractional Integral Operators via Convexity of the Modulus of Derivatives

In this paper, we investigate a class of symmetric Riemann–Liouville‐type fractional integral operators involving a scaling parameter and a fractional order α > −1/2. By establishing a fundamental integral identity based on a symmetric beta‐type kernel, several midpoint‐type inequalities are derived for functions whose derivatives in absolute value are convex. The proposed operators depend on two parameters, namely, the fractional order α and the scaling parameter n , through a unified beta‐type kernel. Their analytical structure allows the derivation of explicit midpoint‐type error estimates expressed in terms of beta and incomplete beta functions. Several numerical examples are included to illustrate the behavior of the resulting bounds for different choices of the parameters. Several classical midpoint‐type identities are recovered as particular cases, showing that the proposed operators provide a unified framework containing the classical Riemann integral setting as a limiting case.