Caputo fractional derivative inequalities for refined modified (h,m)-convex functions

Abstract

In this paper, we introduce a new convex function called refined modified (h,m)−convex function and establish Hadamard-type inequalities for this new definition via Caputo k−fractional derivatives. Then by applying two integral identities including the nth order derivatives of given functions we prove estimation of Hadamard type inequalities for the Caputo k−fractional derivatives.