A Non-Newtonian Noether's Symmetry Theorem

Abstract

The universal principle obtained by Emmy Noether in 1918, asserts that the invariance of a variational problem with respect to a one-parameter family of symmetry transformations implies the existence of a conserved quantity along the Euler-Lagrange extremals. Here we prove Noether's theorem for the recent non-Newtonian calculus of variations. The proof is based on a new necessary optimality condition of DuBois-Reymond type.

This is a preprint of a paper whose final and definite form is published in 'Applicable Analysis', Print ISSN: 0003-6811, Online ISSN: 1563-504X. Submitted 02-Aug-2021, Accepted for publication 22-Nov-2021

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