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Start Over Subject discrete Mittag-Leffler function

1. Note on a discretization of a linear fractional differential equation

Creator:
Čermák, Jan and Kisela, Tomáš
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fractional difference, fractional sum, and discrete Mittag-Leffler function
Language:
English
Description:
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On asymptotics of discrete Mittag-Leffler function

Creator:
Nechvátal, Luděk
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
discrete Mittag-Leffler function, fractional difference equation, asymptotics, and backward h-Laplace transform
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public