Fuzzy Lagrange Polynomials for Solving Two-Dimensional Fuzzy Fractional Volterra Integro-Differential Equations

Abstract

In this study, we present a numerical approach to solve first-order fuzzy fractional Volterra integro-differential equations in two dimensions space, using three different formulations of fuzzy Lagrange polynomials: the fuzzy original Lagrange polynomial (FOLP), the fuzzy barycentric Lagrange polynomial (FBLP), and the fuzzy modified Lagrange polynomial (FMLP). Comprehensive algorithm is constructed to improve the computational efficiency of the proposed method and its effectiveness was tested through numerical application the numerical results demonstrate that the three methods can preserve the basic properties of fuzzy solutions, with the FMLP method achieving superior performance in terms of accuracy in solving the two-dimensional fuzzy fractional integro-differential equation based on the lowest absolute error. To verify the effectiveness of the methods, the resulting numerical solutions were compared graphically with the exact solution.