Abelian and Tauberian results for the fractional Fourier and short-time Fourier transforms of distributions

We introduce the fractional short-time Fourier transform in $ \mathcal S'(\mathbb {R}) $ S & PRIME;(R) and provide generalized asymptotics for the fractional Fourier and the short-time Fourier transforms within $ \mathcal {S}'(\mathbb {R}) $ S & PRIME;(R). Abelian- and Tauberian-type results are given.