Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

A new generalization of the Katugampola generalized fractional integrals in terms of the Mittag-Leffler functions is proposed. Consequently, new generalizations of the Hermite-Hadamard in-equalities by this newly proposed fractional integral operator, for a positive convex stochastic pro-cess, are established. Other known results are easily deduced as particular cases of these inequali-ties. The obtained results also hold for any convex function. Key words and phrases: Hermite-Hadamard inequalities, Mittag-Leffler function, generalized Katugampola fractional integral, convex and positive stochastic process.