New fractional estimates for Hermite-Hadamard-Mercer’s type inequalities

Abstract

An analogous version of Hermite-Hadamard-Mercer’s inequality has been established using the Katugampola fractional integral operators. The result is the generalization of the Riemann-Liouville fractional integral operator combined with the left and right sides of Hermite-Hadamard-Mercer’s involving differentiable mappings whose derivatives in the absolute values are convex. Our main deduction will provide noted existing results in the relative literature. It is shown, that under given conditions the derived integral inequalities, describing some kind of transfer processes, allow an exact solution, expressed by Bessel’s functions, q-digamma function and special bivariate formula. The motivation behind this investigation is to show that it has a potential application in chemical engineering.

Keywords

• Convex function
• Hermite-Hadamard-Mercer inequality
• Jensen Mercer inequality
• Generalized fractional integral operator
• Hölder inequality