# Fractional Herglotz Variational Principles with Generalized Caputo Derivatives

## TL;DR

This paper develops fractional Herglotz variational principles involving generalized Caputo derivatives, deriving Euler-Lagrange equations, transversality conditions, and a Noether-like theorem, with an application to a damped oscillator exhibiting memory effects.

## Contribution

It introduces a new fractional variational framework with generalized derivatives, extending classical principles to systems with memory and damping effects.

## Key findings

- Derived Euler-Lagrange equations for fractional Herglotz problems
- Established a Noether-like symmetry theorem in this context
- Applied the theory to a damped oscillator with variable parameters

## Abstract

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.