In this work, we implement relatively new analytical techniques, the new iterative method (NIM) and homotopy perturbation method (HPM), for solving linear and nonlinear integro-differential equations of fractional derivative order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytical and approximate solutions for different types of fractional differential and integro-differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to integro-differential equations of fractional derivative order.