Mathematical simulation of drug diffusion is a significant tool for predicting the bio-transport process. Moreover, the reported models in the literature are based on Fick's approach, which leads to an infinite propagation speed. Consequently, it is essential to construct a mathematical model to represent the diffusion processes for estimating drug concentrations at different sites and throughout the circulation. Thus, in this article, the diffusion process is employed to propose three models for estimating the drug release from multi-layer cylindrical tablets. A fractional model is presented based on Fick's approach, while classical and fractional Cattaneo models are presented using the relaxed principle. Various numerical methods are used to solve the specified problem. The numerical scheme's stability and convergence are demonstrated. Drug concentration and mass profiles are presented for the tablet and the external medium and compared with the in vivo plasma profiles. The results show the efficiency and precision of the proposed fractional models based on the fourth-order weighted-shifted Grünwald–Letnikov difference operator approximation. These models are compatible with the in vivo data compared with the classical Fick's one.