On Multiparameter Post-Quantum Fractional Quadrature Inequalities with Simulation

This paper introduces a comprehensive class of multiparameter post-quantum fractional quadrature inequalities, unifying classical error bounds within the setting of the post-quantum Riemann–Liouville fractional integral. By incorporating multiple parameters, we derive a flexible family of inequalities that generalize well-known quadrature rules such as the Boole-type, Bullen–Simpson-type, Maclaurin-type, corrected Euler–Maclaurin-type, 38-Simpson-type, and companion Ostrowski-type estimates. Under assumptions of s-convexity, log-convexity, power mean inequality, and Holder inequality, we establish novel error bounds. Our results provide a unified framework for designing and analyzing post-quantum fractional quadrature inequalities. Applications to special means and numerical and graphic examples are presented to illustrate the applicability and generality of the derived inequalities. This work lays a theoretical foundation for the development of post-quantum fractional quadrature inequalities and offers new tools for error estimation in post-quantum fractional-order models arising in applied sciences and engineering.