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