Approximate Solution of Linear Fuzzy Random Ordinary Differential Equations Using Laplace Variational Iteration Method

Ali Adnan Abdulsahib; Fadhel S. Fadhel; Jaafer Hmood Eidi

doi:10.24996/ijs.2024.65.2.18

Authors

Ali Adnan Abdulsahib Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0003-2536-7493
Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
Jaafer Hmood Eidi Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.2.18

Keywords:

Variational iteration method, Laplace transformation, Fuzzy random differential equations, Random differential equations

Abstract

In this article, the Laplace transformation method in connection with the variational iteration method will be used to solve approximately fuzzy random ordinary differential equations. After that, the sequence of approximated closed form iterated solutions is derived based on the general Lagrange multiplier evaluated using the well-known convolution theorem of the Laplace transformation method. In addition, two examples are given and solved to illustrate the reliability, efficiency and applicability of the proposed method, they are simulated using computer programs with two different generations of stochastic processes, namely the Wiener process or Brownian motion, which are 1000 and 10000, respectively.