Fractional Steffensen type inequalities

Abstract

In this article, we state, prove and discuss new Steffensen type fractional inequalities involving fractional derivatives of Canavati, Riemann–Liouville and Caputo types. Finally, we define functionals as a difference between the right- and left-hand sides of the new fractional Steffensen type inequalities and obtain related analogous of the Lagrange and the Cauchy mean value theorems. Furthermore, exponential convexity is proven.

Keywords:

• Steffensen inequality
• Riemann–Liouville fractional integral
• exponential convexity

AMS Subject Classifications::

• Primary 26D10
• Secondary 26D15

Acknowledgements

The authors would like to express our gratitude to careful referees whose valuable advice improved the final version of this article. The research of the authors was supported by the Croatian Ministry of Science, Education and Sports, under the Research Grant No. 117-1170889-0888.