A New Type of Fractional Lie Symmetrical Method and its Applications
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- 作者：Xiao–Tian Zhang ; Jin–Man He ; Shao–Kai Luo
- 关键词：Fractional Lie symmetry ; Conserved quantity ; Fractional generalized Hamiltonian system ; Fractional Duffing oscillator model ; Fractional Lotka biochemical oscillator model
- 刊名：International Journal of Theoretical Physics
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：56
- 期：3
- 页码：971-990
- 全文大小：
- 刊物类别：Physics and Astronomy
- 刊物主题：Physics, general; Quantum Physics; Elementary Particles, Quantum Field Theory; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1572-9575
- 卷排序：56
文摘
In this paper, we present a new type of fractional Lie symmetrical method for finding conserved quantities and explore its applications. For the fractional generalized Hamiltonian system, we introduce a new kind of single-parameter fractional infinitesimal transformation of Lie group in α−1 order space and, under this transformation, give the invariance of the fractional dynamical system and the fractional Lie symmetrical determining equation. Further, a number of important relationships of the fractional Lie symmetrical method are investigated, which reveal the interior properties of the system. By using these relationships, a fractional Lie symmetrical basic integral variable relation and a new fractional Lie symmetrical conservation law are presented. The new conserved quantity is constructed base on fractional Lie symmetrical infinitesimal generators and the interior properties of the system itself, without solving the complicated structural equation. Furthermore, the fractional Lie symmetrical method is applied to the fractional generalized Hamiltonian system of even dimensions. Also, as the new fractional Lie symmetrical method’s applications, we respectively find the conserved quantities of a fractional Duffing oscillator model and a fractional Lotka biochemical oscillator model.