Some New Fractional Weighted Simpson Type Inequalities for Functions Whose First Derivatives Are Convex

Abstract

The goal of this paper is to establish some weighted Simpson type inequalities for functions whose first derivatives are convex involving Reimann–Liouville integral operators. In order to obtain our results, we first prove a new integral identity as an auxiliary result. Based on this identity we establish some fractional weighted Simpson type inequalities for functions whose modulus of the first derivatives are convex. Several special cases are discussed. Error estimates for some numerical quadrature rules are furnished.