A new efficient algorithm to solve non-linear fractional Ito coupled system and its approximate solution

The aim of the present article is to obtain the approximate analytical solution of time fractional Ito coupled equations by using the homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The highlight of the paper is error analysis between the exact solutions and approximate solutions which shows that our approximate solutions converge very rapidly to the exact solutions. The method gives analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The results reveal that the proposed method is very effective and simple.