Fractional Fourier transform in the framework of fractional calculus operators

被引：29
|
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
收藏
页码：779 / 795
页数：17
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