A NOTE ON SIMPSON 3/8 RULE FOR FUNCTION WHOSE MODULUS OF FIRST DERIVATIVES ARE <i>s</i>-CONVEX FUNCTION WITH APPLICATION

Researchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the s-convex functions. Furthermore, we also include the applications to special means.