  We introduce the Segal-Bargmann transform associated to the Mittag Leffler
Fock space and study how it will be connected to the Fourier transform. We will
discuss also the counterpart of the creation and annihilation operator in this
setting using the Caputo and Liouville operators. Finally, we give an extension
of these results to the case of quaternions, in particular in the slice
hyperholomorphic setting.
