Existence of solutions for a nonlinear fractional order differential equation
Let $D^\alpha$ denote the Riemann-Liouville fractional differential operator of order $\alpha$. Let $1 < \alpha < 2$ and $0 < \beta < \alpha$. Define the operator $L$ by $L = D^\alpha - a D^\beta$ where $a \in \mathbb{R}$. We give sufficient conditions for the existence of solutions of t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2009-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=458 |
| _version_ | 1797830726191677440 |
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| author | E. Kaufmann Kouadio D. Yao |
| author_facet | E. Kaufmann Kouadio D. Yao |
| author_sort | E. Kaufmann |
| collection | DOAJ |
| description | Let $D^\alpha$ denote the Riemann-Liouville fractional differential operator of order $\alpha$. Let $1 < \alpha < 2$ and $0 < \beta < \alpha$. Define the operator $L$ by $L = D^\alpha - a D^\beta$ where $a \in \mathbb{R}$. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem
\begin{eqnarray*}
&&Lu(t) + f(t, u(t)) = 0, \quad 0 < t < 1,\\
&&u(0) = 0, \, u(1)= 0.
\end{eqnarray*} |
| first_indexed | 2024-04-09T13:41:47Z |
| format | Article |
| id | doaj.art-93aa9de63a7946a59cf0c996b77a1269 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:47Z |
| publishDate | 2009-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-93aa9de63a7946a59cf0c996b77a12692023-05-09T07:52:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752009-12-012009711910.14232/ejqtde.2009.1.71458Existence of solutions for a nonlinear fractional order differential equationE. Kaufmann0Kouadio D. Yao1University of Arkansas at Little Rock, Little Rock, AR, U.S.A.University of Arkansas at Little Rock, Little Rock, AR, U.S.A.Let $D^\alpha$ denote the Riemann-Liouville fractional differential operator of order $\alpha$. Let $1 < \alpha < 2$ and $0 < \beta < \alpha$. Define the operator $L$ by $L = D^\alpha - a D^\beta$ where $a \in \mathbb{R}$. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem \begin{eqnarray*} &&Lu(t) + f(t, u(t)) = 0, \quad 0 < t < 1,\\ &&u(0) = 0, \, u(1)= 0. \end{eqnarray*}http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=458 |
| spellingShingle | E. Kaufmann Kouadio D. Yao Existence of solutions for a nonlinear fractional order differential equation Electronic Journal of Qualitative Theory of Differential Equations |
| title | Existence of solutions for a nonlinear fractional order differential equation |
| title_full | Existence of solutions for a nonlinear fractional order differential equation |
| title_fullStr | Existence of solutions for a nonlinear fractional order differential equation |
| title_full_unstemmed | Existence of solutions for a nonlinear fractional order differential equation |
| title_short | Existence of solutions for a nonlinear fractional order differential equation |
| title_sort | existence of solutions for a nonlinear fractional order differential equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=458 |
| work_keys_str_mv | AT ekaufmann existenceofsolutionsforanonlinearfractionalorderdifferentialequation AT kouadiodyao existenceofsolutionsforanonlinearfractionalorderdifferentialequation |