On the stretched exponential function and the Havriliak-Negami relaxation

Dielectric relaxation phenomena can be described either in the time or frequency domains. In the time domain, we observe behavior consistent with Debye’s law and a stretched exponential function, whilst in the frequency domain we have the Havriliak-Negami model, which encompasses special cases such as the Cole-Cole and Cole-Davidson models. In my presentation, I shall discuss theoretical results concerning stretched exponential relaxation and Havriliak–Negami-type relaxation. Using Jonscher’s law, which concerns the asymptotic behavior of relaxation and spectral functions, a connection between these types of relaxation can be established. I will also present the causality-composition law and memory-dependent evolution equations, often called the „fractional” evolution equations.