A new computational method for solving the first order linear fuzzy Fredholm integro-differential equations

Abstract

Recently, fuzzy integro-differential equations (FIDEs) have attracted some interest. In this paper, we focus on linear fuzzy Fredholm integro-differential equation and propose a new method for solving it. In fact, using parametric form of fuzzy numbers we convert a linear fuzzy Fredholm integro-differential equation to a linear system of Fredholm integro-differential equations in crisp case. We use variational iteration method (VIM) to obtain solution of this system and hence obtain a fuzzy solution of the linear fuzzy Fredholm integro-differential equation. Finally, using the proposed method, we give some illustrative examples.