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

Nabaa R.  Kareem; Fadhel S.  Fadhel; Sadiq  Al-Nassir

doi:10.6180/jase.202504_28(4).0006

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

Nabaa R. Kareem¹, Fadhel S. Fadhel²This email address is being protected from spambots. You need JavaScript enabled to view it., and Sadiq Al-Nassir³

¹Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

²Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq

³Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

Received: December 28, 2023
Accepted: March 31, 2024
Publication Date: May 29, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202504_28(4).0006

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.

Keywords: Stochastic differential equations, Fuzzy differential equations, Homotopy perturbation method, Brownian motion, Weiner process

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