| Title:
|
Existence and uniqueness of solutions of the fractional integro-differential equations in vector-valued function space (English) |
| Author:
|
Rachid, Bahloul |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
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1212-5059 (online) |
| Volume:
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55 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
97-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this work is to study the existence and uniqueness of solutions of the fractional integro-differential equations $\frac{d}{dt}[x(t) - L(x_{t})]= A[x(t)- L(x_{t})]+G(x_{t})+ \frac{1}{\Gamma (\alpha )} \int _{- \infty }^{t} (t-s)^{\alpha - 1} ( \int _{- \infty }^{s}a(s-\xi )x(\xi ) d \xi )ds+f(t)$, ($\alpha > 0$) with the periodic condition $x(0) = x(2\pi )$, where $a \in L^{1}(\mathbb{R}_{+})$ . Our approach is based on the R-boundedness of linear operators $L^{p}$-multipliers and UMD-spaces. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
$L^{p}$-multipliers |
| Keyword:
|
UMD-spaces |
| MSC:
|
43A15 |
| MSC:
|
45D05 |
| MSC:
|
45N05 |
| idZBL:
|
Zbl 07088761 |
| idMR:
|
MR3964437 |
| DOI:
|
10.5817/AM2019-2-97 |
| . |
| Date available:
|
2019-06-07T14:50:45Z |
| Last updated:
|
2020-02-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147749 |
| . |
| Reference:
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