Some new inequalities for n-polynomial s-type convexity pertaining to inter-valued functions governed by fractional calculus

The main goals of this paper are to provide an introduction to the idea of interval-valued [Formula: see text]-polynomial [Formula: see text]-type convex functions and to investigate the algebraic properties of this type of function. This new generalization aims to show the existence of new Hermite–Hadamard inequalities for the recently presented class of interval-valued [Formula: see text]-polynomials of [Formula: see text]-type convex describing the [Formula: see text]-fractional integral operator. In the classical sense, some special cases are figured out, and the two examples are also given. There are some recently discovered inequalities for interval-valued functions that are regulated by fractional calculus applicable to interval-valued [Formula: see text]-polynomial [Formula: see text]-type convexity. The results obtained show that future research will be simple to implement, highly efficient, feasible, and extremely precise in its investigation. It could also help solve modeling problems, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables.