Homogenization in fractional elasticity

TL;DR

This paper investigates fractional elasticity equations, establishing well-posedness and a homogenization compactness result, while extending the theory to include non-local operators in time and space.

Contribution

It introduces a homogenization framework for fractional elasticity equations, improving existing evolutionary equations theory to handle non-local operators.

Findings

Established well-posedness of fractional elasticity equations

Proved a homogenization compactness result for these equations

Extended the theory to include non-local operators in time and space

Abstract

In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of non-local operators (in time and space).