Exact solutions and numerical study of time fractional Burgers’ equations

Abstract

In this paper, we investigate the exact and numerical solutions of the time fractional Burgers’ equation. By using Cole–Hopf transformation and the method of variables separation, the exact solution is presented in terms of the Mittag-Leffler functions. Moreover, by using the L1-scheme on graded meshes and the Legendre–Galerkin spectral method, the numerical approximation is obtained. A numerical example is presented to confirm all the results.