Fractal-Fractional-Order Modeling of Liver Fibrosis Disease and Its Mathematical Results with Subinterval Transitions
Amjad E. Hamza, Osman Osman, Arshad Ali, Amer Alsulami, Khaled Aldwoah, Alaa Mustafa, Hicham Saber
Abstract
In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This investigation may be referred to as a short memory investigation. Such concepts are useful in problems where a transition is observed when transitioning from one subinterval to the other one. We use the classical and fractal-fractional-order derivative in each subinterval. We study the existence of solutions by using Banach’s and Krasnoselskii’s fixed-point theorems. Their stability is analyzed by adopting the Hyers–Ulam (H-U) stability approach. Also, using the extended Adams–Bashforth–Moulton (ABM) method, we simulate the results that visually present the numerical solutions for different fractal-fractional-order values.