Generalized Hermite-Hadamard Inequalities via (m,n)-Fractional Integrals involving with applications

Abstract

The main objective of this article is to develop some new Hermite-Hadamard type inequalities involving the generalized $(m,n)$-Riemann-Liouville fractional integrals that include the map $\varphi:(0,\infty)\times(0,\infty)\rightarrow[0,\infty]$ satisfying the condition $\varphi(m,m)=m$. Some related inequalities that are closely connected to some known results have been established using the convexity of differentiable functions. We also deduce the some known results from our general results. We will derive the inequalities for the arithmetic, geometric and harmonic $(m,n)$-Riemann-Liouville fractional integral operators.