Analysis of the human liver model through semi-analytical and numerical techniques with non-singular kernel.

This work consists of the study of the time-fractional human liver model with the Caputo-Fabrizio fractional derivative. The existence and uniqueness of the proposed model are shown using fixed point theory. Also, the stability of the considered model is shown using the Ulam Hyres theorem and the Lyapunov function. The solution of the proposed model is obtained using a semi-analytical and numerical scheme. The series solution obtained from the semi-analytical method gives the proper result at any time, similarly, the numerical scheme gives the solution for a long time. The obtained numerical results are compared with real clinical data and earlier published work and found to be very close to real data than earlier published work. Results in the graphs and tables show that the proposed fractional-order model is superior to the traditional model.