Solution Of Linear Fuzzy Stochastic Ordinary Differential Equations Using Homotopy Perturbation Method

The main difficulty of solving fuzzy stochastic ordinary differential equations is that they do not have closed form solution, which represents an exact solution. Therefore, the homotopy perturbation method is proposed in this paper in connection with the method of parametrizing the fuzzy differential equation using-level sets. Thus the problem is converted into two crisp or nonfuzzy stochastic differential equations. We prove that the obtained approximate solution converges to the exact solution as a fuzzy stochastic process and two illustrative examples are considered with fuzziness appears in the initial conditions to be either of triangular or trapezoidal fuzzy numbers. The obtained results show the efficiency and reliability of the followed approach for solving the model problem under consideration.