THERMAL SCIENCE

International Scientific Journal

Jing Li Fu

,

Lijun Zhang

,

Chaudry Masood Khalique

,

Ma Li Guo

MOTION EQUATIONS AND NON-NOETHER SYMMETRIES OF LAGRANGIAN SYSTEMS WITH CONFORMABLE FRACTIONAL DERIVATIVE

ABSTRACT
In this paper, we present the fractional motion equations and fractional non-Noether symmetries of Lagrangian systems with the conformable fractional derivatives. The exchanging relationship between isochronous variation and fractional derivative, and the fractional Hamilton’s principle of the holonomic conservative and non-conservative systems under the conformable fractional derivative are proposed. Then the fractional motion equations of these systems based on the Hamil¬ton’s principle are established. The fractional Euler operator, the definition of fractional non-Noether symmetries, non-Noether theorem, and Hojman’s conserved quantities for the Lagrangian systems are obtained with conformable fractional derivative. An example is given to illustrate the results.
KEYWORDS
non-Noether symmetry, Lagrangian system, Conformable fractional derivative
PAPER SUBMITTED: 2020-05-20
PAPER REVISED: 2020-06-20
PAPER ACCEPTED: 2020-06-20
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200520035F
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1365 - 1372]
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Motion equations and non-Noether symmetries of Lagrangian systems with conformable fractional derivative

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