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Noether’s theorem for fractional variational problems of variable order

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Odzijewicz T., Malinowska A., Torres D.

Open Physics

2013

vol. 11

issue 6

691-701

We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

A discrete time method to the first variation of fractional order variational functionals

100%

Pooseh S., Almeida R., Torres D.

Open Physics

2013

vol. 11

issue 10

1262-1267

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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2 Open Physics

2 2013

2 Torres D.

1 Almeida R.

1 Malinowska A.

1 Odzijewicz T.

1 Pooseh S.

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Noether’s theorem for fractional variational problems of variable order

A discrete time method to the first variation of fractional order variational functionals