Solutions of the mobile-immobile advection-dispersion model based on the fractional operators using the Crank-Nicholson difference scheme

In this manuscript, based on the Atangana-Baleanu Caputo (ABC) fractional derivative and the Caputo fractional derivative for the mobile-immobile advection-dispersion model are considered. For the proposed model, the Crank-Nicholson difference method (C-NDM) scheme is created. Utilizing the Von-Neumann analysis technique, the stability estimate for this difference scheme is demonstrated. The numerical results were obtained for the proposed model using the (C-NDM). The numerical results were produced using the MATLAB program. Then, the obtained approximate solutions for the proposed model through these two fractional derivative operators using the (C-NDM) were compared with the exact solution. The obtained results demonstrate the viability and utility of the proposed technique, and these two fractional derivatives yield a more comparable result. This study differs from previous studies by comparing this model which is based on the Caputo and the Atangana-Baleanu Caputo fractional derivatives using the Crank-Nicholson difference technique.