A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals

This paper deals with a new sharp version of Simpson’s second inequality by using the concepts of absolute continuity, Grüss inequality, and Chebyshev functionals. To demonstrate the applicability of the main result, three examples are given. Also, as generalization of the main result, a Simpson’s second type inequality related to the class of Riemann–Liouville fractional integrals is obtained. In addition, Simpson’s 3/8 formula is applied to approximate the Riemann integral of an absolutely continuous function as well as estimation of approximation error.