New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators
Soubhagya Kumar Sahoo, Y. S. Hamed, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Kamsing Nonlaopon
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.