Fractional variational principle of Herglotz

Ricardo Almeida; Agnieszka B. Malinowska

doi:10.3934/dcdsb.2014.19.2367

Article Contents

2014, Volume 19, Issue 8: 2367-2381. Doi: 10.3934/dcdsb.2014.19.2367

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Fractional variational principle of Herglotz

Ricardo Almeida^1, and
Agnieszka B. Malinowska^2,

1.
CIDMA — Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro
2.
Faculty of Computer Science, Bialystok University of Technology, 15-351 Białystok

Received: March 31, 2014

Revised: March 31, 2014

Published: September 2014

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Abstract

The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought, by differential equations that involve Caputo fractional derivatives. The Euler--Lagrange equations are obtained for the fractional variational problems of Herglotz-type and the transversality conditions are derived. The fractional Noether-type theorem for conservative and non-conservative physical systems is proved.

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Mathematics Subject Classification: Primary: 49K05; Secondary: 26A33.

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