Petrovič Inequality and Its Associated Midpoint- and Trapezoid-Type Estimates with Fractional Extensions for Superquadraticity via Multiplicative Calculus

In this paper, we establish a novel Petrovič-type inequality together with new integral identities for multiplicatively superquadratic functions within the framework of multiplicative calculus. By employing these foundational results, we derive midpoint- and trapezoid-type inequalities for this class of functions, including their fractional analogues formulated via multiplicative Riemann–Liouville fractional operators. The theoretical findings are supported through detailed numerical computations and graphical illustrations, supporting the theoretical results. Furthermore, the applicability of the developed inequalities is demonstrated through representative examples involving special means and the modified Bessel function of type I, thereby highlighting the analytical significance and practical relevance of the obtained results.