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

• Authors: Shakoor Pooseh , Ricardo Almeida , Delfim Torres
• Languages of publication: EN

Abstracts

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.

Keywords

EN

fractional calculus; numerical approximation; discrete time; fractional calculus of variations

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1262-1267

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Shakoor Pooseh

• Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

author

Ricardo Almeida

• Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

author

Delfim Torres

• Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

References

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Identifiers

DOI

10.2478/s11534-013-0250-0