AN EFFICIENT MÜNTZLEGENDRE SPECTRAL GALERKIN METHOD FOR THE TIME-FRACTIONAL BURGERS EQUATION

n this paper, we propose an efficient spectral Galerkin method for the numerical solution of the time-fractional Burgers equation. The method employs Müntz polynomials as basis functions to construct the Galerkin approximation and derive a discrete scheme for the problem. To evaluate its performance, several numerical examples are presented and compared with existing methods. The results demonstrate that the proposed approach achieves high accuracy and efficiency, confirming its potential for solving time-fractional partial differential equations.