An implicit difference method for solving coupled mobile/immobile transport systems with generalized time-fractional operators

This paper introduces an implicit difference scheme for solving a specific class of coupled mobile/immobile transport systems involving generalized time-fractional operators, in which we discretize the derivative with respect to time using the first-order backward difference method. To handle the generalized fractional-order derivative, we employ the L1 discretization formula. We approximate the spatial derivative with the help of the formula for the central difference method. The main contribution of this paper is two-fold. First, the energy method is applied to establish the convergence and stability of an implicit difference scheme under the L∞ norm. Second, we study two examples and provide numerical results to demonstrate the effectiveness of theoretical results we obtained.