Extensions of Simpson’s Inequality via Nonnegative Weight Functions and Fractional Operators

In this paper, we present a new version of Simpson‐type inequalities for differentiable functions defined on a subinterval of the positive real axis. The approach involves a nonnegative integrable weight function and provides an identity that refines the classical Simpson inequality by incorporating the first derivative of the function. A key aspect of this work is the inclusion of the Riemann–Liouville fractional integral, through which we derive specific inequalities that extend the classical framework. In certain cases, our results reduce to the well‐known Simpson inequality, demonstrating the generality and flexibility of the method. MSC2020 Classification: 26A09, 26D10, 26D15, 33E20