Fractional relaxation and the time-temperature superposition principle

Relaxation processes in complex systems like polymers or other viscoelastic materials can be described by equations containing fractional differential or integral operators. In order to give a physical motivation for fractional order equations, the fractional relaxation is discussed in the framework of statistical mechanics. We show that fractional relaxation represents a special type of a non-Markovian process. Assuming a separation condition and the validity of the thermo-rheological principle, stating that a change of the temperature only influences the time scale but not the rheological functional form, it is shown that a fractional operator equation for the underlying relaxation process results.