Non-Debye relaxations: smeared time evolution, memory effects, and the Laplace exponents

DOI10.1016/j.cnsns.2021.105837zbMath1469.78019arXiv2104.06331OpenAlexW3145329349WikidataQ116677384 ScholiaQ116677384MaRDI QIDQ2025576

Tibor K. Pogány, Katarzyna Górska, Andrzej Horzela

Publication date: 14 May 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.06331

zbMATH Keywords

memory functionscompletely monotone and Bernstein functionsnon-Debye relaxation

Mathematics Subject Classification ID

Composite media; random media in optics and electromagnetic theory (78A48) Monotonic functions, generalizations (26A48) Fractional ordinary differential equations (34A08)

Related Items (4)

Subordination and memory dependent kinetics in diffusion and relaxation phenomena ⋮ The Havriliak–Negami and Jurlewicz–Weron–Stanislavsky relaxation models revisited: memory functions based study ⋮ Non-Debye relaxations: the characteristic exponent in the excess wings model ⋮ Duality of fractional systems

Cites Work

• Unnamed Item
• Unnamed Item
• Atypical case of the dielectric relaxation responses and its fractional kinetic equation
• General fractional calculus, evolution equations, and renewal processes
• From Lévy-type processes to parabolic SPDEs. Edited by Lluís Quer-Sardanyons and Frederic Utzet
• Fox function representation of non-Debye relaxation processes
• A note on the equivalence of fractional relaxation equations to differential equations with varying coefficients
• A comment on a controversial issue: a generalized fractional derivative cannot have a regular kernel
• The Volterra type equations related to the non-Debye relaxation
• Anomalous diffusion approach to non-exponential relaxation in complex physical systems
• A note on the article ``Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel
• Justification of the empirical laws of the anomalous dielectric relaxation in the framework of the memory function formalism
• Models of dielectric relaxation based on completely monotone functions
• Applications in Physics, Part B
• The Havriliak–Negami relaxation and its relatives: the response, relaxation and probability density functions
• On complete monotonicity of three parameter Mittag-Leffler function
• Generalized diffusion-wave equation with memory kernel
• Mittag-Leffler Functions, Related Topics and Applications
• The completely monotonic character of the Mittag-Leffler function 𝐸ₐ(-𝑥)
• The representation of 𝑒^{-𝑥^{𝜆}} as a Laplace integral
• Bernstein functions. Theory and applications

This page was built for publication: Non-Debye relaxations: smeared time evolution, memory effects, and the Laplace exponents