The Havriliak–Negami relaxation and its relatives: the response, relaxation and probability density functions

DOI10.1088/1751-8121/aaafc0zbMath1392.82071arXiv1611.06433OpenAlexW2963553882WikidataQ116677395 ScholiaQ116677395MaRDI QIDQ4644123

Katarzyna Górska, Łukasz Bratek, Andrzej Horzela, Giuseppe Dattoli, Karol A. Penson

Publication date: 30 May 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.06433

zbMATH Keywords

Prabhakar functionHavriliak-Negami relaxation(three-parameter) generalized Mittag-Leffler functions

Mathematics Subject Classification ID

Statistical mechanics of polymers (82D60) Mittag-Leffler functions and generalizations (33E12)

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Cites Work

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• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• Fractional models of anomalous relaxation based on the Kilbas and Saigo function
• Viscoelastic properties of a hierarchical model of soft biological tissue: two-dimensional and three-dimensional cases
• The stretched exponential behavior and its underlying dynamics. The phenomenological approach
• Recognition of the ``fractional kinetics in complex systems: dielectric properties of fresh fruits and vegetables from 0.01 to 1.8 ghz
• Dynamic characteristics of the effective susceptibility function in random three-component system
• Anomalous diffusion approach to non-exponential relaxation in complex physical systems
• Models of dielectric relaxation based on completely monotone functions
• Remarks on the stable \(S_{\alpha}(\beta, \gamma, \mu)\) distribution
• Lévy stable distributions via associated integral transform
• On the properties of Laplace transform originating from one-sided Lévy stable laws
• On the function whose Laplace-transform is $e^{-s^{α}}
• Chance and Stability
• Subordinated diffusion and continuous time random walk asymptotics
• Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function
• Computation of the generalized Mittag-Leffler function and its inverse in the complex plane
• Probability distribution built by Prabhakar function. Related Turán and Laguerre inequalities
• The representation of 𝑒^{-𝑥^{𝜆}} as a Laplace integral
• Photoluminescence decay of silicon nanocrystals and Lévy stable distributions