An operational treatment for two-dimensional time-fractional Gray-Scott models

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.