On the generalized Fourier transform

被引：0
|
作者：
Abreu-Blaya, Ricardo [1 ,2 ]
Rodriguez, Jose M. [3 ,4 ]
Sigarreta, Jose M. [1 ]
机构：
[1] Univ Autonoma Guerrero, Fac Matemat, Guerrero, Mexico
[2] Univ UTE, Quito, Ecuador
[3] Univ Carlos III Madrid, Dept Matemat, Madrid, Spain
[4] Univ Carlos III Madrid, Dept Dematemat, Ave Univ 30, Leganes 28911, Madrid, Spain
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 16期
关键词：
fractional derivative; generalized Fourier transform; DEFINITION; MODEL;
D O I：
10.1002/mma.9471
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the new corresponding convolution, inverse and Plancherel formulas, and Hausdorff-Young type inequality. We show that this generalized Fourier transform is useful in the study of several fractional differential equations (both ordinary and partial differential equations).
引用
收藏
页码：16709 / 16733
页数：25
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