Hermite-Hadamard inequality for Hadamard-type fractional integral with respect to a function

Abstract

In this work, we present a new Hermite-Hadamard inequality which is associated with Hadamard-type integral with respect to another function. This fractional integral is the generalization of fractional integral with respect to another function, Hadamard-type fractional integral, Hadamard fractional integral, Tempered fractional integral, Katugam- pola fractional integral and Riemann-Liouville fractional integral. The main signi cance of the inequality is that it contains Hermite-Hadamard inequalities for many fractional integrals as special cases. Generalized result of Hermite-Hadamard type inequality for fractional integral with respect to another function is also established.