Analysis of the zika virus model using the caputo meaning of the Atangana-Baleanu fractional derivative operator

In this study, Zika virus mathematical model has been extended by conducting Atangana -Baleanu fractional derivative with Caputo meaning. Subsequently, the model with the Caputo meaning of the Atangana-Baleanu fractional derivative operator has been subjected to existence-uniqueness solution analysis. After performing the existence solution analysis under the Lipschitz condition, the conditions under which uniqueness solutions are satisfied have been investigated using Picard's uniqueness theorem. The stability analysis of the model has been conducted using the Hyers-Ulam stability theorem. After completing the theoretical solutions, numerical solutions have been obtained using the Adams-Bashforth scheme method developed by Atangana and Owolabi for the Caputo and Atangana-Baleanu operators. These numerical solutions have been demonstrated and compared with numerical simulations, and the results have been presented.