On a Sharp Fractional Integrals Inequality

This paper establishes a new class of sharp trapezoidal-type inequalities for absolutely continuous functions whose derivatives belong to L2a,b. By employing the generalized Chebyshev functional and the framework of Riemann–Liouville fractional integrals, we derive an identity that characterizes the difference between the average of function values at endpoints and its fractional integral. We prove that our obtained bounds are sharp, identifying the optimal constant Dα. The results generalize several known inequalities in the literature by relaxing convexity requirements to absolute continuity. Finally, we provide diverse applications, including a new derivation of Stirling’s formula, refinements of inequalities between special means, and improved error estimates for the trapezoidal quadrature rule.