A Ginzburg–Landau model for material aging depending on temperature

We consider a model describing the behavior of a body subject to aging and fatigue. These phenomena are supposed to be affected by both mechanical and thermal effects. The material is assumed to be viscoelastic where
the stress–strain relation is based on a new fractional derivative proposed in Caputo and Fabrizio. The order of derivative is regarded as a new variable whose evolution is ruled by a Ginzburg–Landau equation. The model also
includes an evolutive equation for the temperature deducing from the first law of thermodynamics. In this article, thermodynamic compatibility is shown and some numerical simulations are performed.