Abstract
The ordinary relaxation phenomenon exhibiting a pure exponential decay is generalized by replacing the first time derivative by the α-fractional derivative (0 < α ⩽ 1) in the basic equation. Mathematical aspects are discussed with emphasis on the related continuous relaxation spectrum. From the physical point of view the thermoelastic coupling in anelastic solids is considered to take into account a temperature fractional relaxation due to diffusion. A viscoelastic model, formerly introduced by Caputo and Mainardi, is then recovered which generalizes the standard linear solid.
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