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Lattice model with power-law spatial dispersion for fractional elasticity

100%

Tarasov V.

Open Physics

2013

vol. 11

issue 11

1580-1588

A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.

The fractional oscillator as an open system

100%

Tarasov V.

Open Physics

2012

vol. 10

issue 2

382-389

A dynamical system governed by equations with derivatives of non-integer order, such as the fractional oscillator, can be considered as an open (non-isolated) system with memory. Fractional equations of motion are obtained from the interaction between the system and the environment with power-law spectral density.

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Lattice model with power-law spatial dispersion for fractional elasticity

The fractional oscillator as an open system