A numerical study of coupled two-dimensional time fractional Burgers equation

Abstract

This thesis presents a numerical study of a coupled system of Burgers equations with conformable fractional derivatives in two dimensions, which is considered difficult to solve due to the overlap between the time fractional derivative and the nonlinear terms in the system. First, we applied the Cole-Hopf transformation to reduce the system to a linear equation of the heat equation type with conformable fractional derivatives in two dimensions. Then, we adopted both explicit and implicit methods to compute the numerical solution of this linear equation. Finally, we obtained a numerical solution of the Burgers equations with conformable fractional derivatives through the combination of the solution of the 2D heat equation and the inverse Cole-Hopf transformation. This study demonstrated the effectiveness of this methodology in finding numerical solutions to such nonlinear problems of fractional nature.