Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 19, Issue 1, Pages 212-228Publisher
SPRINGERNATURE
DOI: 10.1515/fca-2016-0012
Keywords
fractional calculus; Mittag-Leffler type functions; fractional ordinary and pseudo differential equations; dielectric susceptibility; fractional two-power relaxation
Funding
- NCN Maestro Grant [2012/06/A/ST1/00258]
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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.
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