| Title:
|
Functions of finite fractional variation and their applications to fractional impulsive equations (English) |
| Author:
|
Idczak, Dariusz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
171-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak $\sigma $-additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a $\sigma $-additive term---we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures. (English) |
| Keyword:
|
finite fractional variation |
| Keyword:
|
weak $\sigma $-additive fractional |
| Keyword:
|
derivative |
| Keyword:
|
fractional impulsive equation |
| Keyword:
|
Dirac measure |
| Keyword:
|
Cauchy formula |
| MSC:
|
26A45 |
| MSC:
|
34A37 |
| idZBL:
|
Zbl 06738511 |
| idMR:
|
MR3633005 |
| DOI:
|
10.21136/CMJ.2017.0455-15 |
| . |
| Date available:
|
2017-03-13T12:08:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146047 |
| . |
| Reference:
|
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