On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity (Journal of Nonlinear Modeling and Analysis, 2025)
In this study, we introduce a novel hybrid identity that successfullycombines Newton-Cotes and Gauss quadratures, enabling us to recover bothSimpson’s second formula and the left and right Radau 2 point rules, amongothers. Based on this versatile foundation, we establish some new biparametric fractional integral inequalities for functions whose first derivatives areextended $s$-convex in the second sense. To support our findings, we presentillustrative examples featuring graphical representations and conclude withseveral practical applications to demonstrate the effectiveness of our results.
Keywords: Newton-Cotes inequalities; extended $s$-convex functions; Gauss-Radau formula; $P$-functions; hypergeometric function.