Comments on the Properties of Mittag-Leffler Function
Mathematical Physics
2018-08-15 v2 math.MP
Abstract
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schr\"odinger type and heat-type fractional partial differential equations and explore the problem of operatorial ordering finding appropriate rules when non-commuting operators are involved. We discuss the coherent states associated with the fractional Sch\"odinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature.
Cite
@article{arxiv.1707.01135,
title = {Comments on the Properties of Mittag-Leffler Function},
author = {Giuseppe Dattoli and Katarzyna Gorska and Andrzej Horzela and Silvia Licciardi and Rosa Maria Pidatella},
journal= {arXiv preprint arXiv:1707.01135},
year = {2018}
}
Comments
16 pages, 9 figures