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

Abstract

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 inequalities by this newly proposed fractional integral operator, for a positive convex stochastic process, are established. Other known results are easily deduced as particular cases of these inequalities. The obtained results also hold for any convex function.

Keywords

• hermite-hadamard inequalities
• mittag-leffler function
• generalized katugampola fractional integral
• convex and positive stochastic process