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 ¨ older inequality, Power mean inequality and Weighted H ¨ older inequality. This work is motivated by Farid et al in [17]. Especially we aim to obtain inequalities involving only right-sided Caputo-fractional derivative of order α.