@article{Wang2026, 
author = {Xinzhi Wang and Wei Zhang},
title = {Exploring fractional dynamics in the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary condition},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {1},
pages = {55-69},
keywords = {fractional-in-time Gierer-Meinhardt model, pattern formation, numerical method, short-memory principle},
url = {https://www.sciopen.com/article/10.3934/nhm.2026003},
doi = {10.3934/nhm.2026003},
abstract = {This paper presents a new numerical method for simulating the dynamic behavior of the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary conditions. A recursive algorithm for binomial coefficients is introduced, avoiding numerical instabilities associated with Gamma functions. High-precision polynomial expansions and the short-memory principle are employed to enhance efficiency and accuracy. Numerical simulations reveal diverse pattern formation.}
}