New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo-Fabrizio Operator

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.

Automated summary

In this article, a new approach is presented to derive generalized midpoint-type Hermite-Hadamard inequality and Pachpattetype inequality using a new fractional integral operator related to the Caputo-Fabrizio derivative. A new fractional identity for differentiable convex functions of first order is proved. Utilizing these results and various inequalities, new estimations of the Hermite-Hadamard H-H type inequality as refinements are obtained. Applications to special means and trapezoidal quadrature formula are introduced to verify the accuracy of the results.