Lyapunov-type inequalities for a higher order fractional differential equation with fractional integral boundary conditions
New Lyapunov-type inequalities are derived for the fractional boundary value problem \begin{align*} & D_a^\alpha u(t)+q(t)u(t)=0,\quad a<t<b,\\ &u(a)=u'(a)=\dots=u^{(n-2)}(a)=0,\quad u(b)=I_a^{\alpha}(hu)(b), \end{align*} where $n\in \mathbb N$, $n\geq 2$, $n-1<\alpha<n$, $D...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2017-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5513 |
| Summary: | New Lyapunov-type inequalities are derived for the fractional boundary value problem
\begin{align*}
& D_a^\alpha u(t)+q(t)u(t)=0,\quad a<t<b,\\
&u(a)=u'(a)=\dots=u^{(n-2)}(a)=0,\quad u(b)=I_a^{\alpha}(hu)(b),
\end{align*}
where $n\in \mathbb N$, $n\geq 2$, $n-1<\alpha<n$, $D_a^\alpha$ denotes the Riemann--Liouville fractional derivative of order $\alpha$, $I_a^{\alpha}$ denotes the Riemann--Liouville fractional integral of order $\alpha$, and $q,h\in C([a,b];\mathbb R)$. As an application, we obtain numerical approximations of lower bound for the eigenvalues of corresponding equations. |
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| ISSN: | 1417-3875 |