Özet:
This paper focuses on the design and analysis of an efficient numerical method based on the novel implicit finite difference scheme for the solution of the dynamics of reaction-diffusion models. The work replaces the integer first order derivative in time with the Caputo fractional derivative operator. The dynamics of activator-inhibitor as encountered in chemistry, physics and engineering processes, and predator-prey models are two cases addresses in this study. In order to provide a good guidelines on the correct choice of parameters for the numerical simulation of full fractional reaction-diffusion system, its linear stability analysis is also examined. The resulting scheme is applied to solve cross-diffusion problem in two-dimensions. In the experimental results, a number of spatiotemporal and chaotic patterns that are related to Turing pattern are observed. It was discovered in the simulation experiments that the species predator-prey model distribute in almost same fashion, while that of the activator-inhibitor dynamics behaved differently regardless of the value of fractional order chosen. (C) 2020 Elsevier Ltd. All rights reserved.