New Extensions of the Hermite–Hadamard Inequality for Multiplicative Riemann–Liouville Fractional Integrals

In this paper, new lower and upper bounds for the left and right sides of Hermite–Hadamard inequalities involving multiplicative Riemann–Liouville fractional integrals are established by using functions whose second‐order multiplicative derivatives are bounded. Examples are provided for each inequality and supported with two‐dimensional graphs. Moreover, improved and more general forms of Hermite–Hadamard‐type inequalities for multiplicative Riemann–Liouville fractional integrals are presented by employing functions that satisfy the condition (ln f ) ^′ ( a + b − t ) ≥ (ln f ) ^′ ( t ). The results obtained contribute to a more comprehensive understanding of inequalities related to multiplicative fractional integrals.