Fractional Hermite--Hadamard-type inequalities for multiplicatively twice-differentiable functions in multiplicative calculus

This paper investigates a class of Hermite–Hadamard-type fractional inequalities for functions that are multiplicatively twice-differentiable under multiplicative Riemann–Liouville fractional integrals. We first establish a multiplicative fractional Hermite–Hadamard identity, which leads to Hermite–Hadamard-type inequalities. These inequalities are derived under two assumptions: the multiplicative convexity of [Formula: see text] or the convexity of [Formula: see text] ([Formula: see text]). To illustrate the outcomes, some numerical examples of the obtained results are also given.