ATYPICAL CASE OF THE DIELECTRIC RELAXATION RESPONSES AND ITS FRACTIONAL KINETIC EQUATION

作者：Stanislavsky Aleksander^*; Weron Karina^*

来源：Fractional Calculus and Applied Analysis, 2016, 19(1): 212-228.

DOI：10.1515/fca-2016-0012

• fractional calculus
• Mittag-Leffler type functions
• fractional ordinary and pseudo differential equations
• dielectric susceptibility
• fractional two-power relaxation

We present a probabilistic model of the microscopic scenario of dielectric relaxation relating to the atypical case of two-power-law responses. The surveyed approach extends the cluster model concept used for the description of the typical, Havriliak-Negami (HN) law. Within the proposed framework, all empirical two-power-law relaxation patterns may be derived. Their relaxation functions are expressed in terms of the three-parameter Mittag-Leffler function, and the kinetic equation takes the pseudodifferential form generalizing the Riemann-Louiville fractional calculus. This provides a clue to explain the universality observed in relaxation phenomena.

• 出版日期2016-2