Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model
[ X ]
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In 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/).
Açıklama
Anahtar Kelimeler
Fractal operator, Caputo and Caputo-Fabrizio derivatives, Fractional reaction-diffusion, Linear stability analysis, Mittag-Leffler kernel
Kaynak
Alexandria Engineering Journal
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
59
Sayı
4
