| Abstract: |
| The relevance of Noether`s theorem in modern mathematics and physics is out of any doubt, putting in evidence the interplay between mathematical symmetries and laws of nature. Based on previous work by the authors, we explore the existence of Noether`s conserved quantities for restricted fractional dynamics. This kind of dynamics includes fractional derivatives as part of the state space of the relevant Lagrangian functions. Moreover, it accommodates the time evolution of usual Lagrangian systems subject to fractional damping, being the linear damping a particular case. Finally, we also consider particular discretized versions of the fractional restricted dynamics, providing a discrete analog of the previously obtained continuous conserved quantities. |
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