Hybrid Integral Inequalities on Fractal Set

In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the Hölder inequality, the power mean inequality, and a refined version of the latter. Further results are also derived using the concept of generalized concavity. To support our theoretical findings, we provide a graphical example that illustrates the validity of the obtained results, along with some practical applications that demonstrate their effectiveness.