Fractional Herglotz Variational Principles with Generalized Caputo Derivatives

We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects.
Comment: This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', ISSN: 0960-0779. Submitted 16 Dec 2016; Article revised 17 Apr 2017; Article accepted for publication 19 Apr 2017. See [http://dx.doi.org/10.1016/j.chaos.2017.04.035]