On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

被引：25

作者：

Camargo, Rubens Figueiredo ^{[2
]}

de Oliveira, Edmundo Capelas ^{[1
]}

Vaz, Jayme, Jr. ^{[1
]}

机构：

[1] IMECC Unicamp, Dept Matemat Aplicada, BR-13083859 Campinas, SP, Brazil

[2] UNESP, Fac Ciencias, Dept Matemat, BR-17033360 Bauru, SP, Brazil

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2012年 / 15卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Fractional calculus; Mittag-Leffler functions; Integral transforms; H-Fox function; DIFFUSION;

D O I：

10.1007/s11040-011-9100-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler function. As particular cases some recent results are recovered.

引用

页码：1 / 16

页数：16

共 31 条

[1]

[Anonymous], 2007, Numer. Math. J. Chinese Univ. (English Ser.)

[2]

[Anonymous], 1982, H FUNCTION ONE 2 VAR

[3]

[Anonymous], 2010, FRAC CAL APPL ANAL

[4] Differentiation to fractional orders and the fractional telegraph equation [J].

Camargo, R. Figueiredo ;

Chiacchio, Ary O. ;

de Oliveira, E. Capelas .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (03)

[5] On some fractional Green's functions [J].

Camargo, R. Figueiredo ;

Charnet, R. ;

de Oliveira, E. Capelas .

JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (04)

[6]

Capelas de Oliveira E., 2005, ANAL FUNCTIONS APPL

[7]

Capelas de Oliveira E., 2011, FRACTIONAL GRE UNPUB

[8]

Chen W., 2003, ARXIVORGABSMATHPH030

[9] Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics [J].

de Oliveira, E. Capelas ;

Mainardi, F. ;

Vaz, J., Jr. .

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2011, 193 (01) :161-171

[10]

[段俊生 Duan Junsheng], 2004, [高校应用数学学报. A辑, Applied Mathematics a Journal of Chinese Universities], V19, P165

← 1 2 3 4 →