Caputo fractional derivative inequalities via $(h-m)$-convexity

Abstract

The aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of $(h-m)$-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from $(h-m)$-convexity, see Remark \ref{rem1}.