A discrete time method to the first variation of fractional order variational functionals
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- 作者：Shakoor Pooseh (1)
Ricardo Almeida (1)
Delfim F. M. Torres (1) - 关键词：fractional calculus ; numerical approximation ; discrete time ; fractional calculus of variations
- 刊名：Central European Journal of Physics
- 出版年：2013
- 出版时间：October 2013
- 年：2013
- 卷：11
- 期：10
- 页码：1262-1267
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- 作者单位：Shakoor Pooseh (1)
Ricardo Almeida (1)
Delfim F. M. Torres (1)
1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal - ISSN：1644-3608
文摘
The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grünwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.