Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 334, Issue 2, Pages 834-846Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2007.01.013
Keywords
calculus of variations; fractional derivatives; Noether's theorem
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Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being the fractional necessary optimality condition of Euler-Lagrange obtained in 2002. Here we use the notion of Euler-Lagrange fractional extremal to prove a Noether-type theorem. For that we propose a generalization of the classical concept of conservation law, introducing an appropriate fractional operator. (c) 2007 Elsevier Inc. All rights reserved.
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