MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 667-675, 2014

On asymptotics of discrete Mittag-Leffler function

Luděk Nechvátal

Luděk Nechvátal, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic, e-mail:

Abstract: The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional $h$-difference operators) and describe its asymptotics. Here, we shall employ our recent results on stability and asymptotics of solutions to the mentioned equation.

Keywords: discrete Mittag-Leffler function; fractional difference equation; asymptotics; backward $h$-Laplace transform

Classification (MSC 2010): 33E12, 34A08, 39A12

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