Relation between the inverse Laplace transforms of I(tβ) and I(t):: Application to the Mittag-Leffler and asymptotic inverse power law relaxation functions

被引：15

作者：

Berberan-Santos, MN ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Ctr Quim Fis Mol, Inst Super Tecn, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2005年 / 38卷 / 02期

关键词：

Levy distribution; Mittag-Leffler function; Laplace transform; relaxation kinetics;

D O I：

10.1007/s10910-005-5412-x

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

The relation between H(k), inverse Laplace transform of a relaxation function I(t), and H-beta(k), inverse Laplace transform of I(t(beta)), is obtained. It is shown that for beta < 1 the function H-beta(k) can be expressed in terms of H(k) and of the Levy one-sided distribution L-beta(k). The obtained results are applied to the Mittag-Leffler and asymptotic inverse power law relaxation functions. A simple integral representation for the Levy one-sided density function L-1/4(k) is also obtained.

引用

页码：265 / 270

页数：6

共 18 条

[1] Analytical inversion of the Laplace transform without contour integration: application to luminescence decay laws and other relaxation functions [J].

Berberan-Santos, MN .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2005, 38 (02) :165-173

[2] The role of Mittag-Leffler functions in anomalous relaxation [J].

Crothers, DSF ;

Holland, D ;

Kalmykov, YP ;

Coffey, W .

JOURNAL OF MOLECULAR LIQUIDS, 2004, 114 (1-3) :27-34

[3]

Erdelyi A, 1955, HIGHER TRANSCENDENTA, V3

[4]

GLOCKLE WG, 1995, BIOPHYS J, V68, P46, DOI 10.1016/S0006-3495(95)80157-8

[5] FRACTIONAL MASTER-EQUATIONS AND FRACTAL TIME RANDOM-WALKS [J].

HILFER, R ;

ANTON, L .

PHYSICAL REVIEW E, 1995, 51 (02) :R848-R851

[6] Experimental evidence for fractional time evolution in glass forming materials [J].

Hilfer, R .

CHEMICAL PHYSICS, 2002, 284 (1-2) :399-408

[7] Multiple time scales for dispersive kinetics in early events of peptide folding [J].

Metzler, R ;

Klafter, J ;

Jortner, J ;

Volk, M .

CHEMICAL PHYSICS LETTERS, 1998, 293 (5-6) :477-484

[8] When translocation dynamics becomes anomalous [J].

Metzler, R ;

Klafter, J .

BIOPHYSICAL JOURNAL, 2003, 85 (04) :2776-2779

[9] From stretched exponential to inverse power-law: fractional dynamics, Cole-Cole relaxation processes, and beyond [J].

Metzler, R ;

Klafter, J .

JOURNAL OF NON-CRYSTALLINE SOLIDS, 2002, 305 (1-3) :81-87

[10]

Mittag-Leffler G, 1903, CR HEBD ACAD SCI, V137, P554

← 1 2 →