On the Mittag Leffler Bargmann (MLB) transform

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.