Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity

Abstract

Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with Riesz derivatives of non-integer orders. The continuum equations that are obtained from the lattice model describe fractional generalization of non-local elasticity models. Particular solutions and correspondent asymptotic of the fractional differential equations for displacement fields are suggested for the static case.

21 pages, LaTeX, 4 figures

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Review of Some Promising Fractional Physical Models
• Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz Type
• General Lattice Model of Gradient Elasticity

Cited by in corpus (6)

• Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
• Non-Standard Extensions of Gradient Elasticity: Fractional Non-Locality, Memory and Fractality
• Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity
• Fractional Liouville Equation on Lattice Phase-Space
• Large Lattice Fractional Fokker-Planck Equation
• Fractional Diffusion Equations for Lattice and Continuum: Grunwald-Letnikov Differences and Derivatives Approach