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

被引：19

作者：

Stanislavsky, Aleksander ^{[1
,2
]}

Weron, Karina ^{[3
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Radio Astron, 4 Chervonopraporna St, UA-61002 Kharkov, Ukraine

[2] Kharkov Natl Univ, Svobody Sq 4, UA-61022 Kharkov, Ukraine

[3] Wroclaw Univ Technol, Fac Fundamental Problems Technol, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 01期

关键词：

fractional calculus; Mittag-Leffler type functions; fractional ordinary and pseudo differential equations; dielectric susceptibility; fractional two-power relaxation; MITTAG-LEFFLER FUNCTIONS; POWER-LAW; DIFFUSION;

D O I：

10.1515/fca-2016-0012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：212 / 228

页数：17

共 50 条

[1] Atypical Case of the Dielectric Relaxation Responses and its Fractional Kinetic Equation
Aleksander Stanislavsky
Karina Weron
Fractional Calculus and Applied Analysis, 2016, 19 : 212 - 228
[2] The 'fractional' kinetic equations and general theory of dielectric relaxation
Nigmatullin, Raoul R.
PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, VOL 6, PTS A-C, 2005, : 1513 - 1526
[3] Unified fractional kinetic equation and a fractional diffusion equation
Saxena, RK
Mathai, AM
Haubold, HJ
ASTROPHYSICS AND SPACE SCIENCE, 2004, 290 (3-4) : 299 - 310
[4] Unified Fractional Kinetic Equation and a Fractional Diffusion Equation
R.K. Saxena
A.M. Mathai
H.J. Haubold
Astrophysics and Space Science, 2004, 290 : 299 - 310
[5] An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model
Cavus, M. Serdar
JOURNAL OF NON-CRYSTALLINE SOLIDS, 2011, 357 (01) : 202 - 205
[6] Memory kernel formalism with fractional exponents and its application to dielectric relaxation
Hernandez, S. I.
del Castillo, L. F.
del Castillo, Roxana M.
Garcia-Bernabe, Abel
Compan, V.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2023, 612
[7] Dielectric relaxation phenomenon based on the fractional kinetics: theory and its experimental confirmation
Nigmatullin, R. R.
PHYSICA SCRIPTA, 2009, T136
[8] On a class of stochastic fractional kinetic equation with fractional noise
Min Lu
Junfeng Liu
Advances in Difference Equations, 2021
[9] On a class of stochastic fractional kinetic equation with fractional noise
Lu, Min
Liu, Junfeng
ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
[10] The fractional kinetic equation and thermonuclear functions
Haubold, HJ
Mathai, AM
ASTROPHYSICS AND SPACE SCIENCE, 2000, 273 (1-4) : 53 - 63

← 1 2 3 4 5 →