In this work, some analytical techniques viz. homotopy perturbation method, new iterative method and integral iterative method are used to solve nonlinear fractional differential equations such as the equation governing the unsteady flow of a polytropic gas with time-fractional derivative. Comparisons are made between the considered techniques and also between their results. The obtained results reveal that these techniques are very simple and effective and give the solution in series form which in closed form gives the exact solution also, reveal that the integral iterative technique is simpler and shorter in its computational procedures and time than the other techniques.

In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. is combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial di erential equations. ∞ 0 − − , ∈ .

New iterative method; Homotopy perturbation method; Integrodifferential equations of fractional derivative order; Caputo fractional derivative.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 integrodifferential 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.