A fractional-order model of human liver: Analytic-approximate and numerical solutions comparing with clinical data

Abstract

In this work, we aim to propose a mathematical formalism for the human liver involving Caputo fractional derivative (CFD) with modified parameters. Regarding the proposed fractional order model (FOM), the positivity and boundedness theory of an explicit solution are established by using the fractional mean-value theorem in the sense of Caputo. In addition, the validation of the FOM is provided to ensure that it complies with the medical interpretation and we also discuss the stability of unique equilibrium point (EP) for the presented model. We apply the Generalized Mittag–Leffler function method (GMLFM) and Predictor–Corrector method (PCM) to solve this model. The GMLFM is used to give the proper results as a series of the time variable to obtain the desired solution at any time and the PCM is implemented to obtain the solution of the FOM over a long time period. The tabled results from this study are compared with the real clinical data and with other methods. The simulations approximate the real clinical data and support the obtained theoretical results. Precisely, the outcomes of the FOM by using the proposed methods coincide with most of the clinical data that means it more accurate. Ultimately, the graphical results indicate the superiority of the proposed FOM over the classical model.