Application of homotopy analysis method for solving of two-dimensional linear Volterra fuzzy integral equations

摘要

In this paper, we consider the two-dimensional linear Volterra fuzzy integral equation (2D-LVFIE). The homotopy analysis method (HAM) is used for determining the approximated solution of the investigated equation. We convert 2D-LVFIE to a system of linear Volterra integral equation in crisp case. Hence, we obtain an approximate solutions of this system and consequently obtain an approximation for the fuzzy solution of the linear Volterra fuzzy integral equation. We proof the convergence of the proposed method and error estimation between the exact and the approximate solution. A numerical example is given to demonstrate the validity and applicability of the proposed technique.