On the generalized Laplace transform Articles uri icon

publication date

  • April 2021

start page

  • 669

issue

  • 4

volume

  • 13

International Standard Serial Number (ISSN)

  • 2073-8994

abstract

  • 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.

keywords

  • fractional derivative; convolution; generalized laplace transform