Application of the Euler and Runge-Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors

被引：20
作者：
Milici, Constantin [2 ]
Machado, Jose Tenreiro [1 ]
Draganescu, Gheorghe [3 ]
机构：
[1] Polytech Porto, Inst Engn, Dept Elect Engn, R Dr Antonio Bernardino de Almeida 431, P-4249015 Porto, Portugal
[2] Polytech Univ Timisoara, Dept Math, Timisoara, Romania
[3] West Univ Timisoara, Res Ctr Theoret Phys, Timisoara, Romania
来源：
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2020年 / 21卷 / 02期
关键词：
fractional differential equations; Euler method; Runge-Kutta method; Caputo derivative; Lorenz fractional attractor; Taylor generalized formula; Lyapunov exponent; stability;
D O I：
10.1515/ijnsns-2018-0248
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper applies the Euler and the fourth-order Runge-Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.
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页码：159 / 170
页数：12
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