Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity
arXiv:1502.05492 · doi:10.1016/j.ijsolstr.2014.04.014
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.
arXiv comment21 pages, LaTeX, 4 figures
References in corpus (10)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Fractional dynamics of systems with long-range interaction
- Review of Some Promising Fractional Physical Models
- Continuous Limit of Discrete Systems with Long-Range Interaction
- Map of Discrete System into Continuous
- Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions
- Universal Electromagnetic Waves in Dielectric
- Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz Type
- General Lattice Model of Gradient Elasticity
- Fractional Gradient Elasticity from Spatial Dispersion Law
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