Author(s): HE Shengxin, ZHU Jianqing, ZHANG Yi, School of Mathematics and Physics, SUST, School of Civil Engineering, SUST
Pages: 11-17
Year: 2016 Issue:  3
Journal: Journal of Suzhou Railway Teachers College, Natural Science Edition
Keyword:  fractional Lagrange system; Caputo fractional derivative; Noether symmetry; conserved quantity;
Abstract: This paper has proposed and studied the Noether symmetries and the conserved quantities for frac-tional Lagrange systems based on combined Caputo fractional derivatives. Firstly, the fractional Hamilton varia-tional principle for the Lagrange systems was established, and the fractional Lagrange equations were obtained.Secondly, based upon the invariance of the fractional Hamilton action under the infinitesimal transformation of groups, we provided the definition and criterion of the fractional Noether symmetry transformation and the frac-tional Noether quasi-symmetry transformation for the system. Finally, the relation between the fractional Noether symmetries and the conserved quantities was established. At the end of the paper, two examples were given to il-lustrate the application of the results.