Mild and classical solutions to a fractional singular second order evolution problem
Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fra...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1530 |
| _version_ | 1797830628916330496 |
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| author | Nasser-Eddine Tatar |
| author_facet | Nasser-Eddine Tatar |
| author_sort | Nasser-Eddine Tatar |
| collection | DOAJ |
| description | Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fractional derivatives. This term may be regarded also as a fractional integral of that regular function. In addition the initial conditions are nonlocal and involve fractional derivatives too. |
| first_indexed | 2024-04-09T13:40:13Z |
| format | Article |
| id | doaj.art-266eca30476b497180141276de57a5e9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:13Z |
| publishDate | 2012-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-266eca30476b497180141276de57a5e92023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-11-0120129112410.14232/ejqtde.2012.1.911530Mild and classical solutions to a fractional singular second order evolution problemNasser-Eddine Tatar0King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaExistence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term. The non-local term is an integral in the form of a convolution of a singular kernel and a regular function involving fractional derivatives. This term may be regarded also as a fractional integral of that regular function. In addition the initial conditions are nonlocal and involve fractional derivatives too.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1530cauchy problemcosine familyfractional derivativefractional non-local conditionsmild solutionssecond-order abstract problem |
| spellingShingle | Nasser-Eddine Tatar Mild and classical solutions to a fractional singular second order evolution problem Electronic Journal of Qualitative Theory of Differential Equations cauchy problem cosine family fractional derivative fractional non-local conditions mild solutions second-order abstract problem |
| title | Mild and classical solutions to a fractional singular second order evolution problem |
| title_full | Mild and classical solutions to a fractional singular second order evolution problem |
| title_fullStr | Mild and classical solutions to a fractional singular second order evolution problem |
| title_full_unstemmed | Mild and classical solutions to a fractional singular second order evolution problem |
| title_short | Mild and classical solutions to a fractional singular second order evolution problem |
| title_sort | mild and classical solutions to a fractional singular second order evolution problem |
| topic | cauchy problem cosine family fractional derivative fractional non-local conditions mild solutions second-order abstract problem |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1530 |
| work_keys_str_mv | AT nassereddinetatar mildandclassicalsolutionstoafractionalsingularsecondorderevolutionproblem |