Pattern is a non-uniform macro structure with some regularity in space or time, which is
common in nature. In this manuscript, we introduce the Fourier transform for spatial …

In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear
coupled FitzHugh–Nagumo model. Numerical simulation is carried out to elucidate the …

A reaction–diffusion system can be represented by the Gray–Scott model. The reaction–
diffusion dynamic is described by a pair of time and space dependent Partial Differential …

In this work, the solution of Riesz space fractional partial differential equations of parabolic
type is considered. Since fractional-in-space operators have been applied to model …

This paper explores the suitability of space fractional-order reaction–diffusion scenarios to
model some emergent pattern formation in predator–prey models. Such fractional reaction …

Abstract The Gray-Scott model is the representative bistable system in many reaction–
diffusion models. Numerical simulation of this model is very difficult especially for space …

In this paper, we propose efficient and reliable numerical methods to solve two notable non-
integer-order partial differential equations. The proposed algorithm adapts the Fourier …

The generalized fractional reaction–diffusion equations which exist in the form of noninteger
order partial differential equations have now found wide application for illustrating important …

Abstract The Gray–Scott (GS) model represents the dynamics and steady state pattern
formation in reaction–diffusion systems and has been extensively studied in the past. In this …

This paper proposes the computational approach for fractional-in-space reaction-diffusion
equation, which is obtained by replacing the space second-order derivative in classical …