Numerical solutions of time and space fractional coupled Burgers equations using time-space Chebyshev pseudospectral method

The aim of the paper is to develop and analyze a spectrally accurate time-space pseudospectral method to the approximate solution of nonlinear time and space fractional coupled Burgers equations. Liouville-Caputo fractional derivative formula is used to evaluate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivative matrices, the given problem is reduced to a system of nonlinear algebraic equations. A mapping is used to transform the nonhomogeneous initial-boundary values to homogeneous initial-boundary values. Error analysis of the proposed method for the equation is presented. A model example of fractional coupled Burgers equations is tested for a set of fractional-order derivatives. For the proposed method, highly accurate numerical results are obtained, which confirm the accuracy and efficiency of the proposed method.