Simpson-like inequalities for functions whose third derivatives belong to $s$-convexity involving Atangana--Baleanu fractional integrals and their applications

Abstract

The main objective of this paper is to study Simpson-like inequalities by using the Atangana--Baleanu (AB) fractional integral operators for functions whose third derivatives of absolute values are $s$-convex. To begin with, we establish the parameterized integral identity. As an effect of this outcome, we derive a series of Simpson-like integral inequalities related to functions whose third derivatives belong to the $s$-convexity in absolute values. Furthermore, an improved version of the identity is given and the estimated results are obtained by considering boundedness and Lipschitz condition. It concludes with some applications in respect of the Simpson-like quadrature formulas and special means, separately.