Fractional Hermite–Hadamard Inequalities in Non-Newtonian Calculus Focusing on h-GG-Convex Functions

The aim of this paper is to develop new Hermite–Hadamard–type inequalities within the framework of fractional GG-multiplicative calculus. By employing the GG-multiplicative Riemann–Liouville fractional integral operators, we introduce a novel class of generalized convex functions, called h-GG-convex functions, which unifies and extends several existing notions of convexity in non-Newtonian calculus. Under suitable assumptions on the auxiliary function h, including the class of B-functions, we establish new fractional Hermite–Hadamard inequalities for h-GG-convex functions defined on positive intervals. The obtained results generalize previously known inequalities for GG-convex, s-GG-convex, and P-functions-GG-convex mappings as special cases. Moreover, by choosing particular values of the fractional order, our results reduce to the classical Hermite–Hadamard inequality in the multiplicative setting. These findings enrich the theory of fractional inequalities in G-calculus and provide a flexible framework for further developments in non-Newtonian analysis.