Map of Discrete System into Continuous

Abstract

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of long-range interactions are considered. The discrete equations of motion are mapped into the continuum equation with the Riesz fractional derivative.

32 pages, LaTeX

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Cited by in corpus (19)

• Fractional Vector Calculus and Fractional Maxwell's Equations
• Review of Some Promising Fractional Physical Models
• Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
• Map of Discrete System into Continuous
• Fractional Power-Law Spatial Dispersion in Electrodynamics
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• Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity
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• Power-law Spatial Dispersion from Fractional Liouville Equation
• Weyl Quantization of Fractional Derivatives
• A fractional generalization of the classical lattice dynamics approach
• Fractional Derivative Regularization in QFT
• Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach
• Fractional Stability
• Biquaternionic Reformulation of a Fractional Monochromatic Maxwell System