多独立变量的分数阶变分法
数学物理
2013-10-14 v1 math.MP
最优化与控制
摘要
我们证明了广义分数阶导数与积分的多维分部积分公式。新结果使我们能够获得拉格朗日量依赖于广义偏积分和导数的多维分数阶变分问题的最优性条件。文中给出了广义分数阶 Noether 定理、Dirichlet 原理的表述以及一个唯一性结果。
引用
@article{arxiv.1308.4585,
title = {Fractional Calculus of Variations of Several Independent Variables},
author = {Tatiana Odzijewicz and Agnieszka B. Malinowska and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1308.4585},
year = {2013}
}
备注
This is a preprint of a paper whose final and definite form is published in Eur. Phys. J. Special Topics 222 (2013), 1811-1824. DOI: 10.1140/epjst/e2013-01966-0 Paper submitted 05-Dec-2012; revised 06-May-2013; accepted 15-May-2013