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Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator

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El-Nabulsi R.
Open Physics
|
2011
|
vol. 9
|
issue 1
250-256
EN
The purpose of this paper is to extend the fractional actionlike variational approach by introducing a generalized fractional derivative operator. The generalized fractional formalism introduced through this work includes some interesting features concerning the fractional Euler-Lagrange and Hamilton equations. Additional attractive features are explored in some details.
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A discrete time method to the first variation of fractional order variational functionals

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Pooseh S., Almeida R., Torres D.
Open Physics
|
2013
|
vol. 11
|
issue 10
1262-1267
EN
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.
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