https://doi.org/10.1140/epjst/e2018-00073-1
Regular Article
Comments on the properties of Mittag-Leffler function
1
ENEA – Frascati Research Center,
Via Enrico Fermi 45,
00044
Frascati, Rome, Italy
2
H.Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences,
ul.Eliasza – Radzikowskiego 152,
31342
Krakow, Poland
3
Dep. of Mathematics and Computer Science, University of Catania,
Viale A. Doria 6,
95125
Catania, Italy
a e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
9
August
2017
Received in final form:
18
December
2017
Published online: 25
July
2018
Abstract
The properties of Mittag-Leffler function are 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 Schrödinger 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 Schödinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature.
© EDP Sciences, Springer-Verlag 2018
