Abstract
In this article, a generalized midpoint-type Hermite-Hadamard inequality and Pachpattetype inequality via a new fractional integral operator associated with the Caputo-Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Holder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard H-H type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.