In this paper, we investigate the generalized Milne-type integral inequalities via the framework of generalized [Formula: see text]-convex mappings on fractal sets. To accomplish this, we propose a new generalized integral identity that involves differentiable generalized [Formula: see text]-convex mappings. Based on the latest identity we drive a number of the latest fractal Milne-type integral inequalities. Also, we provide fractal Milne-type inequalities for bounded mappings. Some illustrative examples and applications to additional inequalities for the generalized special means and various error estimates for the generalized Milne-type quadrature formula are obtained to further support our results. The findings presented in this research offer important generalizations and extensions of previous work in the field.

In this work, we address and explore the concept of generalized m-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate the current initiated idea. Furthermore, we prove the latest variant of Hermite-Hadamard type inequality employing the proposed definition of preinvexity. We also derive several novel versions of inequalities of the Hermite-Hadamard type and Fejér-Hermite-Hadamard type for the first-order local differentiable generalized m-preinvex functions. Finally, some new inequalities for the generalized means and generalized random variables are established as applications.