In this paper, the double fuzzy Sumudu transform (DFST) method was used to find the solution to partial Volterra fuzzy integro-differential equations (PVFIDE) with convolution kernel under Hukuhara differentiability. Fundamental results of the double fuzzy Sumudu transform for double fuzzy convolution and fuzzy partial derivatives of the n-th order are provided. By using these results the solution of PVFIDE is constructed. It is shown that DFST method is a simple and reliable approach for solving such equations analytically. Finally, the method is demonstrated with examples to show the capability of the proposed method.

The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM). The studied equation is converted to a nonlinear system of Volterra-Fredholm integral equations in a crisp case. Approximate solutions of this system are obtained by the help with HAM and hence an approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integral equation is presented. The convergence of the proposed method is proved and the error estimate between the exact and the approximate solution is obtained. The validity and applicability of the proposed method is illustrated on a numerical example.

In the present paper, we propose an efficient iterative numerical method of successive approximations to approximate solution of nonlinear Urisohn-Volterra fuzzy functional integral equations by fuzzy trapezoidal quadrature formula for classes of fuzzy-number-valued functions of Lipschitz type. We prove the convergence of the method and investigate the numerical stability of the present method with respect to the choice of the first iteration. The convergence of the method is tested through a numerical experiment, that confirms the obtained theoretical results.

A numerical method for solving two-dimensional nonlinear Volterra fuzzy integral equation (2D-NVFIE) of the second kind will is introduced. We convert a nonlinear Volterra fuzzy integral equation to a nonlinear system of Volterra integral equation in crisp case. We use Adomian Decomposition Method (ADM) to find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear Volterra fuzzy integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed method are proved. Some numerical examples are included to demonstrate the validity and applicability of the proposed technique.