Many problems which appear in different sciences such as physics, engineering, biology, applied mathematics and different branches can be modeled by using deterministic integral equations. Weakly singular integral equation is one of the principle type of integral equations which was introduced by Abel for the first time. These problems are often dependent on a noise source which are neglected due to poor computational tools. So, it is satisfactory to use stochastic models to describe the behaviour of them. Thus, researchers added uncertainty term in the deterministic models and this leads to the stochastic models such as stochastic partial differential equations or stochastic integral equations. Since 1960, by increasing computational power, some random factors are inserted to deterministic integral equations and are created various kinds of stochastic integral equations such as Ito-Volterra integral equations, Ito-Fredholm integral equations, or weakly singular Ito-Volterra integral equations. In more cases, the analytical solution of these equations do not exist or finding their analytic solution is very difficult. Thus, presenting an accurate numerical method is an essential requirement in numerical analysis. Numerical solution of stochastic integral equations because the randomness has its own difficulties. In recent years, some different basis functions have been used to estimate the solution of stochastic integral equations. In this paper, we develop operational matrix method based on Euler polynomials to solve weakly singular Ito-Volterra integral equations. Euler polynomials have received considerable attention in dealing with various problems and equations.
