Analysis of Keller-Segel Model with Atangana-Baleanu Fractional Derivative

Abstract

The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.