A Note on Fractional Parametric-Type Laplace Transforms

In recent articles an extension of the exponential function including one or several parameters have been exploited to introduce generalized forms of linear dynamical systems, including population dynamics models, and some graphical curves and Chebyshev functions. In this article, by means of the Blissard problem we define the reciprocal of parametric or fractional parametric-type exponentials in order to define new-type Laplace transforms. Some examples are shown, derived by the second author using the computer algebra system Mathematica.