On the Sheffer-type polynomials related to the Mittag-Leffler functions: applications to fractional evolution equations
- Resource Type
- Working Paper
- Authors
- Górska, K.; Horzela, A.; Penson, K. A.; Dattoli, G.
- Source
- Subject
- Mathematical Physics
- Language
We present two types of polynomials related to the Mittag-Leffler function namely the fractional Hermite polynomial and the Mittag-Leffler polynomial. The first modifies the Hermite polynomial and the second one is a refashioned Laguerre polynomial. The fractional Hermite and the Mittag-Leffler polynomials are used to solve {the Cauchy problems for} the fractional Fokker-Planck equation where the fractional derivative is taken in the Caputo sense with respect to time and/or space. The generating functions of these two kinds of polynomials are also calculated and they indicate that these polynomials belong to the Sheffer type.