A NEW SPECTRAL ALGORITHM FOR TIME SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH SUBDIFFUSION AND SUPERDIFFUSION
This paper reports a new spectral collocation algorithm for solving time space fractional partial differential equations with subdiffusion and superdiffusion. In this scheme we employ the shifted Legendre Gauss Lobatto collocation scheme and the shifted Chebyshev Gauss Radau collocation approximations for spatial and temporal discretizations, respectively. We focus on implementing the new algorithm for two physical problems, namely, time fractional modified anomalous subdiffusion and fractional nonlinear superdiffusion equations. The numerical results obtained by using this algorithm have been compared with another numerical scheme in order to demonstrate the high accuracy and efficiency of the proposed method.