Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method

In this paper, by introducing the fractional derivative in the sense of Caputo, the generalized two-dimensional differential transform method (DTM) is directly applied to solve the coupled Burgers equations with space- and time-fractional derivatives. The presented method is a numerical method based on the generalized Taylor series formula which constructs an analytical solution in the form of a polynomial. Several illustrative examples are given to demonstrate the effectiveness of the generalized two-dimensional DTM for the equations.