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 Mittag-Leffler functions is proposed. Consequently, generalizations Hermite-Hadamard inequalities by this newly proposed integral operator, for a positive convex stochastic process, are established. Other known results easily deduced as particular cases these inequalities. The obtained also hold any function.