Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative

被引：39

作者：

Owolabi, Kolade M. ^{[1
,2
]}

机构：

[1] Univ Free State, Fac Nat & Agr Sci, Inst Groundwater Studies, ZA-9300 Bloemfontein, South Africa

[2] Fed Univ Technol Akure, Dept Math Sci, PMB 704, Akure, Ondo State, Nigeria

来源：

CHAOS SOLITONS & FRACTALS | 2018年 / 115卷

关键词：

Mittag-Leffler; Fractional derivative; Hopf-bifurcation; Oscillations; Predator-prey; Stability analysis; REACTION-DIFFUSION EQUATIONS; ORDER; KERNEL; MODELS;

D O I：

10.1016/j.chaos.2018.08.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the mathematical analysis and numerical simulation of time-fractional multicomponent systems. Here, the classical time derivatives in such systems are replace with the Atangana-Baleanu fractional derivative in the sense of Caputo. This derivative is found useful in the sense that it combines both the non-local and nonsingular kernels in its formulation. A two-step family of Adams-Bashforth method is derived for the approximation of the Atangana-Baleanu derivative. Numerical experiments presented for different instances of alpha, 0 < alpha <= 1 correspond to our theoretical findings. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：127 / 134

页数：8

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