In this paper, a generalized fuzzy barycentric Lagrange interpolation method is proposed to solve two-dimensional fuzzy fractional Volterra integral equations. Firstly, we use the generalized Gronwall inequality and iterative methods to demonstrate the existence and uniqueness of solutions to the original equation. Secondly, combining the generalized fuzzy interpolation method and the fuzzy Gauss-Jacobi quadrature formula to discretize the original equation into corresponding algebraic equations in fuzzy environment. Then, the convergence of the proposed method is analyzed, and an error estimate is given based on the uniform continuity modulus. Finally, some numerical experiments show that the proposed method has high numerical accuracy for both smooth and non-smooth solutions.

本文提出了一种广义模糊重心拉格朗日插值方法来求解二维模糊分式Volterra积分方程。首先，我们利用广义Gronwall不等式和迭代方法证明了原方程解的存在性和唯一性。其次，结合广义模糊插值法和模糊高斯-雅可比求积公式，将原方程离散化为模糊环境下相应的代数方程。然后，分析了该方法的收敛性，并给出了基于均匀连续模的误差估计。最后，数值实验表明，该方法对于光滑解和非光滑解均具有较高的数值精度。