Solvability of the Fractional Hyperbolic Keller-Segel System

We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which describes the random motion of a certain population due a substance concentration. Considering the initial-boundary value problem for the fractional hyperbolic Keller-Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.