  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.
