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The Hamilton formalism with fractional derivatives. (English) Zbl 1104.70012

Summary: Recently the traditional calculus of variations has been extended to be applicable to systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton’s equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, and the results obtained are in exact agreement with Agrawal formalism.

MSC:

70H05 Hamilton’s equations
26A33 Fractional derivatives and integrals
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