Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis

TL;DR

This paper investigates how boundary conditions affect fractional chemotaxis models, deriving approximations for boundary layers and interior solutions to better understand nonlocal boundary interactions in biological systems.

Contribution

It introduces a method to analyze boundary effects in fractional chemotaxis equations, providing first-order approximations for boundary layers and interior solutions under reflection conditions.

Findings

Derived boundary layer and interior solutions using perturbation theory.

Provided insights into boundary effects in nonlocal fractional chemotaxis models.

Enhanced understanding of boundary interactions in fractional diffusion processes.

Abstract

In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary conditions within a nonlocal fractional framework. Using boundary layer methods and perturbation theory, we derive first-order approximations for interior and boundary layer solutions under symmetric reflection conditions. This work provides fundamental insights into the complex interplay between fractional dynamics, chemotactic transport phenomena, and boundary interactions, opening future research in biological and physical applications involving nonlocal processes.