Fractional Herglotz variational principles with generalized Caputo derivatives
Copyright policy )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.
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]
- UNIVERSIDADE DE AVEIRO Portugal
- Sapienza University of Rome Italy
- University of Aveiro Portugal
- University of Leeds United Kingdom
- Roma Tre University Italy
Optimality conditions for free problems in one independent variable, fractional variational principles, FOS: Physical sciences, Euler–Lagrange equations, Fractional ordinary differential equations, Mathematical Physics (math-ph), 26A33, 49K05, 49S05, Fractional variational principles, Euler–Lagrange equations; Fractional variational principles; Generalized fractional operators; Herglotz problem, generalized fractional operators, Fractional derivatives and integrals, Optimization and Control (math.OC), Oscillation theory of functional-differential equations, FOS: Mathematics, Herglotz problem, Euler-Lagrange equations, Generalized fractional operators, Variational principles of physics, Mathematics - Optimization and Control, Functional-differential equations with fractional derivatives, Mathematical Physics
Optimality conditions for free problems in one independent variable, fractional variational principles, FOS: Physical sciences, Euler–Lagrange equations, Fractional ordinary differential equations, Mathematical Physics (math-ph), 26A33, 49K05, 49S05, Fractional variational principles, Euler–Lagrange equations; Fractional variational principles; Generalized fractional operators; Herglotz problem, generalized fractional operators, Fractional derivatives and integrals, Optimization and Control (math.OC), Oscillation theory of functional-differential equations, FOS: Mathematics, Herglotz problem, Euler-Lagrange equations, Generalized fractional operators, Variational principles of physics, Mathematics - Optimization and Control, Functional-differential equations with fractional derivatives, Mathematical Physics
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