On the Generalized Laplace Transform

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Bosch, Paul
Carmenate García, Héctor José
Rodríguez, José Manuel
Sigarreta, José María
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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.
Palabras clave
Fractional derivative , Convolution , Generalized Laplace transform
Bosch, P.; Carmenate García, H.J.; Rodríguez, J.M.; Sigarreta, J.M. On the Generalized Laplace Transform. Symmetry 2021, 13, 669. https://doi.org/10.3390/ sym13040669