The purpose of this work is to achieve the analytic solution of non-linear Liouville-Caputo fractional initial value problem including time fractional Rosenau–Hyman equation by means of ARA transform and iterative method. First of all, ARA transform is employed to reduce the problem into a simpler one. Then the series solution of the non-linear fractional initial value problem is acquired by applying iterative method which leads to the analytic solution of the Rosenau–Hyman equation (RHE) with initial condition. The obtained results verify that the combination of ARA transform with iterative method produces an effective method to tackle with non-linear fractional problems.
