New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions

Abstract

The main motivation of this study is to present new Hermite-Hadamard (HH) type inequalities via a certain fractional operators. We establish two new identities and give new estimations of HH- type inequalities for differentiable and convex mapping via Katugampola-fractional operators. Here, we gave new Lemmas having identities for differentiable functions and construct related inequalities. Main findings of this study would provide elegant connections and general variants of well known results established recently. These results can be extended to different kinds of convex functions as well as pre-invex functions.

Keywords

• Convex functions
• Hermite-Hadamard inequalities
• Katugampola-fractional integrals

References

1. A. Kilbas, H.M. Srivastava and J.J. Trujillo,Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, Netherlands, (2006). K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, (1993). H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamar-Fejer type inequalityies for generalized fractional integrals , J.Math. Anal. Appl. , 26(2013), 742-753.