Fractional Fourier transform in the framework of fractional calculus operators

被引：30

作者：

Kilbas, A. A. ^{[2
]}

Luchko, Yu. F. ^{[1
]}

Martinez, H. ^{[3
]}

Trujillo, J. J. ^{[4
]}

机构：

[1] Tech Univ Appl Sci, Dept Math 2, D-13353 Berlin, Germany

[2] Belarusian State Univ, Fac Math & Mech, Minsk 220050, BELARUS

[3] Natl Expt Univ Guayana, Port Ordaz, State Bolivar, Venezuela

[4] Univ La Laguna, Dept Anal Matemat, E-38207 San Cristobal la Laguna, Tenerife, Spain

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2010年 / 21卷 / 10期

关键词：

Fourier and fractional Fourier transforms; modified Liouville fractional derivatives and integrals; operational relations; diffusion-type fractional differential equation; Laplace transform; Mittag Leffler function; LIZORKIN-TYPE; DENSENESS;

D O I：

10.1080/10652461003676099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is devoted to the study of a fractional Fourier transform in a special space of functions by Lizorkin. Connections of such a transform with differentiation operators are established and an inverse operator for such a transform if constructed. Compositions of the fractional Fourier transform with modified fractional integrals and derivatives are proved. Application to solution of a partial diffusion-type differential equation of fractional order is given.

引用

页码：779 / 795

页数：17

共 18 条

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