Analytical solutions of fuzzy initial value problems by HAM

In this paper, series solution of fuzzy initial value problems under strongly generalized differentiability by means of the homotopy analysis method is considered. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Although the homotopy analysis method contains the auxiliary parameter, the convergence region of the series solution can be controlled in a simple way. The proposed technique is applied to a few test examples to illustrate the accuracy and applicability of the method. The results reveal that the method is very effective and straightforward. Meanwhile, analysis results show that the homotopy analysis method is a powerful and easy-to-use analytic tool to solve fuzzy initial value problems.