FRACTIONAL VARIATIONAL PRINCIPLE OF HERGLOTZ

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.