A Computational Approach for Fractal Mobile-Immobile Transport with Caputo-Fabrizio Fractional Derivative

This paper deals with a spectral collocation method for the numerical solution of linear and nonlinear fractal Mobile/Immobile transport (FM/IT) model with Caputo-Fabrizio fractional derivative (C-F-FD). In the time direction, the finite difference procedure is used to construct a semi-discrete problem and afterwards by applying a Chebyshev-spectral method, we obtain the approximate solution. The unconditional stability of the proposed method is proved which provides the theoretical basis of proposed method for solving the considered equation. Finally, some numerical experiments are included to clarify the efficiency and applicability of our proposed concepts in the sense of accuracy and convergence ratio.