Solvability of the Fractional Hyperbolic Keller-Segel System

TL;DR

This paper establishes the solvability of a fractional hyperbolic Keller-Segel model for chemotaxis, using fractional calculus and kinetic formulations, advancing mathematical understanding of nonlocal population dynamics.

Contribution

It introduces a new nonlocal approach to modeling chemotaxis and proves the solvability of the fractional hyperbolic Keller-Segel system.

Findings

Proves the existence of solutions for the fractional hyperbolic Keller-Segel model.

Utilizes fractional calculus and kinetic formulations in the analysis.

Provides a mathematical foundation for nonlocal chemotaxis models.

Abstract

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.