In this study, fractional order mathematical modelling of the human liver using the Caputo fraction derivative is considered. This model was divided into two compartments, Bromsulphthalein (BDP) content in blood (Z) and Bromsulphthalein (BDP) content in liver (W). The Caputo derivative was used as the fractional derivative. A stability analysis was performed on the fractional-order mathematical model of the human liver. The system’s existence, uniqueness and non-negativity were analysed mathematically. Numerical solutions were obtained using the Generalized Euler method and interpreted graphically.