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arXiv · 1912.10728

On the Sheffer-type polynomials related to the Mittag-Leffler functions: applications to fractional evolution equations

K. Górska·A. Horzela·K. A. Penson·G. Dattoli
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Abstract

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.

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K. Górska, A. Horzela, K. A. Penson, G. Dattoli. 2019-12-23. On the Sheffer-type polynomials related to the Mittag-Leffler functions: applications to fractional evolution equations. https://arxiv.org/abs/1912.10728

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