About the kinetic description of fractional diffusion equations modeling chemotaxis

Source abstract

In this paper, we are interested in the microscopic description of fractional diffusion chemotactic models. We will use the kinetic framework of collisional equations having a heavy-tailed distribution as equilibrium state and take an adequate hydrodynamic scaling to deduce the fractional Keller–Segel system for the cell dynamics. In addition, we use this frame to deduce some models for chemotaxis with fractional diffusion including biological effects and non-standard drift terms.