@article{Ezz-Eldien2026, 
author = {Samer S. Ezz-Eldien and Ali H. Tedjani and Amra Al Kenany and Marwa Alzubaidi},
title = {An operational treatment for two-dimensional time-fractional Gray-Scott models},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {5246-5269},
keywords = {Legendre polynomial, spectral collocation method, operational matrix, fractional differential equations, Gray-Scott model},
url = {https://www.sciopen.com/article/10.3934/math.2026215},
doi = {10.3934/math.2026215},
abstract = {Due to the poor regularity of solutions to time-fractional partial differential equations, traditional spectral approaches typically suffer from significant accuracy reductions when applied in the time domain. To overcome this problem, in this paper, we applied a spectral approach based on a new set of basis functions, which are smooth in the spatial direction and non-smooth in the time direction. The spectral collocation approach was used combined with the operational matrix approach based on the new set of basis functions to solve two-dimensional time-fractional Gray-Scott models. Applying the operational technique reduces the computations of the full scheme and achieves significant accuracy by using a small number of these functions. Numerical results confirmed the high accuracy of the proposed approach when applied for smooth and non-smooth solutions.}
}