On the Generalized Laplace Transform

被引：6

作者：

Bosch, Paul ^{[1
]}

Carmenate Garcia, Hector Jose ^{[2
]}

Manuel Rodriguez, Jose ^{[3
]}

Maria Sigarreta, Jose ^{[2
]}

机构：

[1] Univ Desarrollo, Fac Ingn, Ave Plaza 680, Santiago 7550000, Chile

[2] Univ Autonoma Guerrero, Fac Matemat, Ctr Acapulco, Calle Chilpancingo, Acapulco De Juarez 39610, Guerrero, Mexico

[3] Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Madrid 28911, Spain

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 04期

关键词：

fractional derivative; convolution; generalized Laplace transform; DEFINITION; FEATURES; MODEL;

D O I：

10.3390/sym13040669

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations.

引用

页数：14

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