Sinc-Legendre collocation method for the non-linear Burgers' fractional equation

This paper deals with the numerical solution of the nonlinear fractional Burgers' equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The solution is based on using the Sinc method, which builds an approximate solution valid on the entire spatial domain, and in the time domain, we use the shifted Legendre polynomials to replace the time fractional derivatives. The error in the approximation is shown to converge to the exact solution at an exponential rate. Illustrative examples are given with an applications from traffic flow, and the numerical results are shown to demonstrate the efficiency of the newly proposed method.