# American Institute of Mathematical Sciences

October  2014, 19(8): 2367-2381. doi: 10.3934/dcdsb.2014.19.2367

## Fractional variational principle of Herglotz

 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, Poland

Received  April 2014 Revised  April 2014 Published  August 2014

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.
Citation: Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367
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