Ogunmez, HasanSarikaya, Mehmet Zeki2025-10-112025-10-1120251687-91201687-9139https://doi.org/10.1155/admp/7710785https://hdl.handle.net/20.500.12684/21788In 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, 33E20en10.1155/admp/7710785info:eu-repo/semantics/openAccessconvex functionSimpson inequality and fractional operatorweight functionsArticle202512-s2.0-105014509015WOS:001559152900001Q2Q3