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

Abstract

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.