Study of a Continuous Fractional-Order Dynamical System of Fibrosis of Liver

In this manuscript, our objective is to develop a fractional-order linear model (FOLM) that characterizes the behavior of the human liver, specifically focusing on the dynamics of bromsulphthalein storage and transfer, particularly in the context of chronic alcoholic liver disease. To achieve this, we employ a novel approach utilizing non-orthogonal Bernstein polynomials to construct operational matrices. These matrices play a crucial role in describing the fractional-order coupled dynamics within the human liver system. We assessed the presence and stability of a solution through the utilization of well-established fractional calculus findings. Drawing from precise clinical data, we present numerical instances accompanied by graphical representations illustrating the fractional order dynamics inherent in our proposed model. To reinforce the credibility and efficacy of our novel approach, we conclude with a contrastive analysis against integer-order outcomes. The resultant matrix equation, stemming from the fractional operational matrices, is systematically elucidated utilizing the computational capabilities of the mathematical software Matlab. This step unveils the intricate details of the transformed system, shedding light on the underlying dynamics.