The Laplace transform in discrete fractional calculus

In this paper, we introduce a new two-dimensional fractional Stockwell transform using the kernel of the coupled fractional Fourier transform. We establish that the two-dimensional fractional Stockwell transform satisfies all the expected ...${\mathcal{}}^{\mathrm{}}{\mathbb{}}^{\mathrm{}}$

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse ...

Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These ...