New Majorized Fractional Simpson Estimates

Abstract

Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function. Practicing majorization theory, we formulate a new auxiliary identity by utilizing fractional integral operators. In order to obtain new bounds, we employ the idea of convex functions on the Niezgoda–Jensen–Mercer inequality for majorized tuples, along with some fundamental inequalities including the Hölder, power mean, and Young inequalities. Some applications to the quadrature rule and examples for special functions are provided as well. Interestingly, the main findings are the generalizations of many known results in the existing literature.