Some new Caputo fractional derivative inequalities for exponentially (θ,h−m)–convex functions

Abstract

Firstly, we obtain some inequalities of Hadamard type for exponentially (θ,h−m)–convex functions via Caputo k–fractional derivatives. Secondly, using integral identity including the (n+1)–order derivative of a given function via Caputo k-fractional derivatives we prove some of its related results. Some new results are given and known results are recaptured as special cases from our results.

Keywords

• hermite–hadamard inequality
• caputo k-fractional derivatives
• hölder's inequality
• exponentially (θ，h−m)–convex functions