@article{Dai2022, 
author = {Dan-Dan Dai and Wei Zhang and Yu-Lan Wang},
title = {Numerical simulation of the space fractional    (  3  +  1  )-dimensional Gray-Scott models with the Riesz fractional derivative},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10234-10244},
keywords = {numerical simulation, patterns, Fourier spectral method, Riesz fractional derivative},
url = {https://www.sciopen.com/article/10.3934/math.2022569},
doi = {10.3934/math.2022569},
abstract = {The reaction-diffusion process always behaves extremely magically, and any a differential model cannot reveal all of its mechanism. Here we show the patterns behavior can be described well by the fractional reaction-diffusion model (FRDM), which has unique properties that the integer model does not have. Numerical simulation is carried out to elucidate the attractive properties of the fractional (3+1)-dimensional Gray-Scott model, which is to model a chemical reaction with oscillation. The Fourier transform for spatial discretization and fourth-order Runge-Kutta method for time discretization are employed to illustrate the fractal reaction-diffusion process.}
}