| Title:
|
On asymptotics of discrete Mittag-Leffler function (English) |
| Author:
|
Nechvátal, Luděk |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
667-675 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
discrete Mittag-Leffler function |
| Keyword:
|
fractional difference equation |
| Keyword:
|
asymptotics |
| Keyword:
|
backward $h$-Laplace transform |
| MSC:
|
33E12 |
| MSC:
|
34A08 |
| MSC:
|
39A12 |
| idZBL:
|
Zbl 06433690 |
| idMR:
|
MR3306856 |
| DOI:
|
10.21136/MB.2014.144143 |
| . |
| Date available:
|
2015-02-04T09:27:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144143 |
| . |
| Reference:
|
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