Hamiltonian formalism of fractional systems

Abstract

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional equations of motion are derived using the Hamiltonian formalism. The approach is illustrated with a simple-fractional oscillator in a free state and under an external force. Besides the behavior of the coupled fractional oscillators is analyzed. The natural extension of this approach to continuous systems is stated. The interpretation of the mechanics is discussed.

16 pages, 5 figures

References in corpus (7)

• Fractional diffusion modeling of ion channel gating
• Fractional oscillator
• Fractional dynamics from the ordinary Langevin equation
• Levy model for interstellar scintillations
• Twist of fractional oscillations
• Black-Scholes model under subordination
• Beam propagation in a Randomly Inhomogeneous Medium

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• Broadening quantum cosmology with a fractional whirl
• Homogeneous fractional embeddings