Fractional integral approaches to weighted corrected Euler–Maclaurin-type inequalities for different classes of functions

In recent years, a wide variety of integral inequalities, including Newton-type, Simpson-type, and corrected Euler–Maclaurin-type inequalities, have been extensively studied, particularly in the framework of fractional calculus using Riemann–Liouville or conformable fractional integrals. Among these, fractional corrected Euler–Maclaurin-type inequalities have emerged as a valuable tool due to their improved approximation capabilities. In this study, we focus on developing weighted corrected Euler–Maclaurin-type inequalities for different classes of functions using Riemann–Liouville fractional integrals. To achieve this, we first derive a key integral equality with the aid of a positive weighted function, providing the foundation for the primary outcomes. Through the use of this integral equality, we prove new inequalities for differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. Also, for better explanation, we offer some examples together with their matching graphs. Moreover, these findings extend previous results. Consequently, the study clarifies the significance of corrected Euler–Maclaurin-type inequalities and suggests opportunities for further exploration.