 Noether’s theorem for fractional Birkhoffian system of Herglotz type with time delayJuan-Juan Ding and Yi Zhang Chaos, Solitons & Fractals, 2020, vol. 138, issue C Abstract: Noether symmetry theorem of Herglotz type for time-delayed fractional Birkhoffian system are studied. Firstly, based on the fractional derivative of Riemann-Liouville, the Herglotz variational principle of time-delayed fractional Birkhoffian system is established, and the time-delayed Birkhoff′s equation of Herglotz type is derived. Secondly, the definition and criterion of Herglotz type Noether symmetric transformation of time-delayed fractional Birkhoffian system are established. Thirdly, the Noether′s theorem of the system is proposed and proved, in addition, the inner relationship between Noether symmetries and conservation is accurately explored. Next, the special case of the theorem is discussed, in other words, when the Herglotz generalized variational principle is reduced to the classical variational principle, the result of this paper is degraded into the Noether symmetry theorem of the time-delayed fractional Birkhoffian system. Finally, an example is given. Keywords: Noether symmetry; Herglotz generalized variational principle; fractional Birkhoffian system; Conserved quantity; Riemann-Liouville fractional derivative (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303131 DOI: 10.1016/j.chaos.2020.109913 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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