2007/11/05 by Gastão S. F. Frederico, Gastao S. F. Frederico, Delfim F. M. Torres · 1 citation
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons #math-ph #math.MP #math.OC #msc:26A33 #msc:49K05 #msc:70H33
paper · pdf · doi:10.1007/s11071-007-9309-z
published as Nonlinear Dynamics, Vol. 53, No. 3, 2008, pp. 215--222. · The original publication is available at http://www.springerlink.com Nonlinear Dynamics
arxiv created 2007/11/05 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum, and the fractional derivative of the state variable.