A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative

Abstract

• A new fractional model of human liver is proposed. • A parameter modification is employed to avoid dimensional mismatching. • The existence of a unique solution is investigated. • A new and efficient numerical method is suggested, and its convergence is explored. • A comparison is made between the predicted values by the model and the clinical data. In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelöf approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.