Owolabi, Kolade M.Atangana, AbdonAkgul, Ali2024-12-242024-12-2420201110-01682090-2670https://doi.org/10.1016/j.aej.2020.03.022https://hdl.handle.net/20.500.12604/6296In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations. As a case study, the fractal fractional Schnakenberg system is formulated with the Caputo operator (in terms of the power law), the Caputo-Fabrizio operator (with exponential decay law) and the Atangana-Baleanu fractional derivative (based on the Mittag-Liffler law). We design some algorithms for the Schnakenberg model by using the newly proposed numerical methods. In such schemes, it worth mentioning that the classical cases are recovered whenever alpha = 1 and beta = 1. Numerical results obtained for different fractal-order (beta is an element of (0, 1)) and fractional-order (alpha is an element of (0, 1)) are also given to address any point and query that may arise. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).eninfo:eu-repo/semantics/openAccessFractal operatorCaputo and Caputo-Fabrizio derivativesFractional reaction-diffusionLinear stability analysisMittag-Leffler kernelArticle59424772490Q1WOS:000563768600021Q12-s2.0-8508274242710.1016/j.aej.2020.03.022