On the existence of positive solutions for a local fractional boundary value problem with an integral boundary condition
In this work, we are concerened with the fractional differential equation \begin{displaymath} D^{\alpha}_{0^+} u(t)+f(t,u(s))=0,\quad 1<\alpha\leq 2 \end{displaymath} where $D^\alpha_{0^+}$ is the standard Riemann-Liouville fractional derivative, subject to the local boundary conditions \...
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| Natura: | Articolo |
| Lingua: | English |
| Pubblicazione: |
Sociedade Brasileira de Matemática
2020-10-01
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| Serie: | Boletim da Sociedade Paranaense de Matemática |
| Accesso online: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/40065 |
| Riassunto: | In this work, we are concerened with the fractional differential equation
\begin{displaymath}
D^{\alpha}_{0^+} u(t)+f(t,u(s))=0,\quad 1<\alpha\leq 2
\end{displaymath}
where $D^\alpha_{0^+}$ is the standard Riemann-Liouville fractional derivative, subject to the local boundary conditions
\begin{displaymath}
u(0)=0,\quad u(1)+\int_0^\eta u(t)dt=0, \quad 0\leq \eta< 1.
\end{displaymath}
We try to obtain the existence of positive solutions by using some fixed point theorems.
\end{abstract}
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| ISSN: | 0037-8712 2175-1188 |