 Generic
Number - 1402 |
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| Written
Date -
January 17th, 13 |
| Modified
Date -
January 17th, 13 |
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| Summary |
The method of upper and lower solutions and the generalized
quasilinearization technique is developed for the existence and
approximation of solutions to boundary value problems for higher
order fractional differential equations of the type
\begin{equation*}
\begin{split}
&{}^{c}\mathcal{D}^{q}u(t)+f(t,u(t))=0,\hspace{0.4 cm} t\in(0,1),
q\in(n-1,n],\,n\geq
2\\&
u'(0)=0, u''(0)=0,..., u^{n-1}(0)=0,u(1)=\xi u(\eta),
\end{split}
\end{equation*}
where $\xi,\,\eta\in (0,1)$,
the nonlinear function $f$ is assumed to be continuous and
${}^{c}\mathcal{D}^{q}$ is the
fractional derivative in the sense of Caputo. Existence of solution
is established via the upper and lower solutions method and
approximation of solutions uses the generalized quasilinearization
technique. |
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Three-point boundary value problems for higher order nonlinear fractional differential equations
