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arXiv · 1802.10544

A Fractional Variational Approach for Modelling Dissipative Mechanical Systems: Continuous and Discrete Settings

Fernando Jiménez·Sina Ober-Blöbaum
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Abstract

Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional Euler-Lagrange equations (both in the continuous and discrete settings), which, as we show, are invariant under linear change of variables. This principle relies on a particular restriction upon the admissible variation of the curves. In the case of the half-derivative and mechanical Lagrangians, i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange equations model a dissipative system in both directions of time, summing up to a set of equations that is invariant under time reversal. Finally, we show that the discrete equations are a meaningful discretisation of the continuous ones.

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Fernando Jiménez, Sina Ober-Blöbaum. 2018-02-28. A Fractional Variational Approach for Modelling Dissipative Mechanical Systems: Continuous and Discrete Settings. https://arxiv.org/abs/1802.10544

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