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A formulation of Noether’s theorem for fractional problems of the calculus of variations. (English) Zbl 1119.49035
The authors extend classical results from calculus of variations to the context of fractional differentiation. They use the notion of Euler-Lagrange fractional extremal in order to extend a Noether-type theorem to problems having fractional derivatives. They also propose a generalization of the classical concept of conservation law. In their analysis, the authors use the results from [O. P. Agrawal, J. Math. Anal. Appl. 272, No. 1, 368–379 (2002; Zbl 1070.49013)].
49S05Variational principles of physics
26A33Fractional derivatives and integrals (real functions)
70S10Symmetries and conservation laws