A Pseudospectral Method for solving a variable order time fractional diffusion equation

In this paper, a pseudospectral method with the Lagrange polynomial basis on Chebyshev points is proposed to solve the variable order time fractional diffusion equations (VOTFDEs). This method is based on the evaluation of the Mittag-Leffler function on matrix arguments for the integration along the time variable to preserve the high accuracy of the spectral method. Some examples are performed to illustrate the accuracy and efficiency of the proposed method.