{"paper":{"title":"Fractional Gradient Elasticity from Spatial Dispersion Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Vasily E. Tarasov","submitted_at":"2013-06-11T16:16:32Z","abstract_excerpt":"Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the fractional generalization of gradient elasticity that allows us to describe a weak non-locality of power-law type. We suggest a lattice model with spatial dispersion of power-law type as a microscopic model of fractional gradient elastic continuum. We prove that the continuous limit maps the equations for lattice with this spatial dispersion into the continuum equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2572","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}