HIERARCHICAL ANALOGS TO FRACTIONAL RELAXATION EQUATIONS

Recently fractional calculus has become an important tool in the analy sis of slow relaxation phenomena, such as stress-strain relationships in polymeric materials. In the rheological constitutive equations this implies the replacement of the first-order derivatives by fractional derivatives. Here we show that such procedures have hierarchical mecha nical analogues. We focus on the generalized dashpot and the generaliz ed Maxwell model and display the corresponding arrangements. Our model s allow a transparent interpretation of the parameters which enter the fractional equations, and reveal that the internal dynamics are hiera rchically constrained.