Justification of the empirical laws of the anomalous dielectric relaxation in the framework of the memory function formalism

DOI10.2478/s13540-014-0165-5zbMath1312.78007OpenAlexW2057033684MaRDI QIDQ2347405

Ivan I. Popov, A. A. Khamzin, Raoul R. Nigmatullin

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-014-0165-5

zbMATH Keywords

fractalsdielectric permittivityfractional calculus operatorsfractal kineticsCole-Davidson expressionCole-Cole expressionHavriliak-Negami expression

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Statistical mechanics of polymers (82D60) Fractional derivatives and integrals (26A33) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Mittag-Leffler functions and generalizations (33E12) Linear constitutive equations for materials with memory (74D05) Composite media; random media in optics and electromagnetic theory (78A48) Fractals (28A80)

Related Items (12)

Anomalous Relaxation in Dielectrics with Hilfer Fractional Derivative ⋮ Models of dielectric relaxation based on completely monotone functions ⋮ Adaptive fuzzy synchronization of fractional-order chaotic (hyperchaotic) systems with input saturation and unknown parameters ⋮ The Havriliak–Negami and Jurlewicz–Weron–Stanislavsky relaxation models revisited: memory functions based study ⋮ Stability of fractional-order systems with Prabhakar derivatives ⋮ Memory kernel formalism with fractional exponents and its application to dielectric relaxation ⋮ Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models ⋮ The Volterra type equations related to the non-Debye relaxation ⋮ Exploring the applications of fractional calculus: hierarchically built semiflexible polymers ⋮ Non-Debye relaxations: smeared time evolution, memory effects, and the Laplace exponents ⋮ Anomalous diffusion approach to non-exponential relaxation in complex physical systems ⋮ Chaos in the fractional order nonlinear Bloch equation with delay

Cites Work

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• Microscopic model of a non-Debye dielectric relaxation: the Cole-Cole law and its generalization
• The derivation of the generalized functional equations describing self-similar processes
• Microscopic model of dielectric \(\alpha\)-relaxation in disordered media
• Generalized mittag-leffler function and generalized fractional calculus operators
• Fractional Kinetics in Solids
• Memory Effects in Irreversible Thermodynamics

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