Analysis of hepatitis B virus model with Atangana-Baleanu fractional operator

In this thesis, the solution of the extended model was investigated by applying the hepatitis B virus model (Ullah ve dig., 2019) to the Atangana-Baleanu fractional derivative (Atangana ve Baleanu, 2016). Afterwards, the entity solution of this model applied to the Atangana-Baleanu fractional derivative operator is done. After the existence solution is realized, the situations in which uniqueness solutions are provided are examined with the help of Picard's uniqueness theorems. After completing the theoretical solutions, numerical solutions produced by Atangana and Owolabi (Atangana ve Owolabi, 2018) for Caputo and Atangana-Baleanu operators were applied to the model. Numerical solutions were made and the results were written and finalized by showing and comparing them with simulations.