A generalized fuzzy barycentric Lagrange interpolation method for solving two-dimensional fuzzy fractional Volterra integral equations

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.