New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators

Abstract

The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of two convex functions on fractional integrals. Also, we consider a new identity for differentiable mappings in the context of the Caputo-Fabrizio fractional integral operators. Then, considering this identity as an auxiliary result, some new related H-H-M type inequality with the assistance of Hölder, power-mean, Young, and Hölder-İşcan inequality are presented. Finally, we give some applications of modified Bessel functions and matrices, and we also discuss some future scopes.