Development of a computational approach for a space–time fractional moving boundary problem arising from drug release systems

Studying a time‐fractional moving boundary diffusion model of solvent through a glassy polymer: A computational approach

“…To calculate δt 1 , we use Equation (32), boundary condition (26), and c 1 0 ¼ 1 for k ¼ 0 as follows…”

“…Among the analytical and numerical approaches that have been used to solve these problems, we can refer to the refined integral method, the heat balance integral method (HBIM), the variational iteration method, the homotopy perturbation method, the boundary immobilization method (BIM), finite element and finite difference methods. 18,19,[31][32][33][34][35][36] The model under investigation has been developed for cases of classical diffusion with spherical and slab geometries using numerical methods and asymptotic methods such as the combined integral method (CIM) and the heat balance integral method (HBIM). These studies have considered short and long diffusion times by assuming constant diffusion coefficient and linear diffusion.…”

“…Since the nature of moving boundary problems is nonlinear, there are few analytical approaches to solve them. Among the analytical and numerical approaches that have been used to solve these problems, we can refer to the refined integral method, the heat balance integral method (HBIM), the variational iteration method, the homotopy perturbation method, the boundary immobilization method (BIM), finite element and finite difference methods 18,19,31–36 …”

“…Here, due to the existence of the initial condition , by fixing the boundary, we will encounter a singularity in . In this study, we use an iterative non‐standard finite difference approach to determine the unknown moving boundary and the solvent concentration 18,19,32 . For our interest problem, the authors could not find any numerical or analytical solution to compare the results.…”

“…In this study, we use an iterative non-standard finite difference approach to determine the unknown moving boundary and the solvent concentration. 18,19,32 For our interest problem, the authors could not find any numerical or analytical solution to compare the results. Here, we inevitably presented only the numerical results for different values of parameters.…”