(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
In this study, we introduce a novel hybrid identity that successfully combines Newton-Cotes and Gauss quadratures, enabling us to recover both Simpson’s second formula and the left and right Radau 2 point rules, among others. Based on this versatile foundation, we establish some new biparametric fractional integral inequalities for functions whose first derivatives are extended s-convex in the second sense. To support our findings, we present illustrative examples featuring graphical representations and conclude with several practical applications to demonstrate the effectiveness of our results.