Existence, stability, and numerical simulations of a fractal-fractional hepatitis B virus model

Abstract

This paper uses a new fractal-fractional operator with a power law-type kernel in the Riemann-Liouville sense to formulate the new fractal-fractional model of hepatitis B virus (HBV) transmission with asymptomatic carriers. The existence of the model’s solutions is demonstrated using Schuder’s fixed point theorem. The Banach fixed point theorem is utilized to prove the uniqueness of the solutions. Solutions’ stability behaviors in the Ulam concept are also discussed. Further, using the newly created numerical scheme based on Newton’s polynomial, the new numerical scheme for HBV is created. Numerical simulations show the accuracy of the approximate solutions of the new numerical method, along with the clear effect of the fractal dimension and fractional order on the spread of the HBV disease.