Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives

被引：0

作者：

Frederico, Gastao S. F. ^{[1
,2
]}

Torres, Delfim F. M. ^{[2
]}

机构：

[1] Gregorio Semedo Univ, Luanda, Angola

[2] Univ Aveiro, Ctr Res & Dev Math & Applicat, Dept Math, Aveiro 3810193, Portugal

来源：

2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC) | 2012年

关键词：

calculus of variations; optimal control; fractional derivatives; Euler-Lagrange equations; invariance; Noether's theorem; VARIATIONAL CALCULUS; CONSERVATION-LAWS; LINEAR VELOCITIES; FORMULATION; TERMS;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/ fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives.

引用

页码：6885 / 6890

页数：6

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