NEW FRACTIONAL-TYPE INEQUALITIES FOR GENERALIZED n-POLYNOMIAL CONVEXITY IN INTERVAL-VALUED FUNCTIONS

In this paper, we introduce and investigate a new class of functions known as generalized [Formula: see text]-polynomial interval-valued convex functions. Our study focuses on exploring fractional calculus-based Hermite–Hadamard [Formula: see text]-fractional integral inequalities, Hermite–Hadamard–Fej[Formula: see text]r-type [Formula: see text]-fractional integral inequalities, and various product inequalities. These results extend the classical Hermite–Hadamard integral inequalities by incorporating fractional calculus. Additionally, we provide numerical examples and graphical analyses to validate and clarify our theoretical findings. This work offers insights into the dynamic interplay between fractional calculus, polynomial convexity, and fractal geometry within interval-valued functions, contributing to both theoretical understanding and potential future advancements in this area of mathematical research.