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Fecha
2021-07-15
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info:eu-repo/semantics/openAccess
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American Institute of Mathematical Sciences
Citas
Resumen
We prove a Noether's theorem of the first kind for the so-called restricted fractional Euler-Lagrange equations and their discrete counterpart, introduced in [26,27], based in previous results [11,35]. Prior, we compare the restricted fractional calculus of variations to the asymmetric fractional calculus of variations, introduced in [14], and formulate the restricted calculus of variations using the discrete embedding approach [12,18]. The two theories are designed to provide a variational formulation of dissipative systems, and are based on modeling irreversbility by means of fractional derivatives. We explicit the role of time-reversed solutions and causality in the restricted fractional calculus of variations and we propose an alternative formulation. Finally, we implement our results for a particular example and provide simulations, actually showing the constant behaviour in time of the discrete conserved quantities outcoming the Noether's theorems.
Descripción
The registered version of this article, first published in Journal of Geometric Mechanics, is available online at the publisher's website: American Institute of Mathematical Sciences, https://doi.org/10.3934/jgm.2021012
La versión registrada de este artículo, publicado por primera vez en Journal of Geometric Mechanics, está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, https://doi.org/10.3934/jgm.2021012
La versión registrada de este artículo, publicado por primera vez en Journal of Geometric Mechanics, está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, https://doi.org/10.3934/jgm.2021012
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Citación
Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2022). Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations. Journal of Geometric Mechanics, 14(1), 57-89. https://doi.org/10.3934/JGM.2021012
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I