Several new integral inequalities via Caputo fractional integral operators

Abstract

In this paper, we establish several new integral inequalities including
Caputo fractional derivatives for quasi--convex, $s-$Godunova--Levin convex.
In order to obtain our results, we have used fairly elementary methodology
by using the classical inequalities such that H\"{o}lder inequality, Power
mean inequality and Weighted H\"{o}lder inequality. This work is motivated by Farid et al in \cite{farid-naqvi}. Especially we aim to obtain inequalities involving only right-sided Caputo-fractional derivative of order $\alpha$.