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Fractional conservation laws in optimal control theory. (English) Zbl 1170.49017
Summary: 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.
MSC:
49K10Free problems in several independent variables (optimality conditions)
26A33Fractional derivatives and integrals (real functions)
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