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 Model. Anal. Inform. Sist., 2016, Volume 23, Number 3, Pages 370–376 (Mi mais508)

A Caputo two-point boundary value problem: existence, uniqueness and regularity of a solution

M. Stynes

Beijing Computational Science Research Center, Haidian District, Beijing 100193, China

Abstract: A two-point boundary value problem on the interval $[0,1]$ is considered, where the highest-order derivative is a Caputo fractional derivative of order $2-\delta$ with $0<\delta <1$. A necessary and sufficient condition for existence and uniqueness of a solution $u$ is derived. For this solution the derivative $u'$ is absolutely continuous on $[0,1]$. It is shown that if one assumes more regularity — that $u$ lies in $C^2[0,1]$ — then this places a subtle restriction on the data of the problem.

Keywords: fractional derivative, boundary value problem, existence, uniqueness, regularity.

DOI: https://doi.org/10.18255/1818-1015-2016-3-370-376

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UDC: 517.9
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Citation: M. Stynes, “A Caputo two-point boundary value problem: existence, uniqueness and regularity of a solution”, Model. Anal. Inform. Sist., 23:3 (2016), 370–376

Citation in format AMSBIB
\Bibitem{Sty16} \by M.~Stynes \paper A Caputo two-point boundary value problem: existence, uniqueness and regularity of a solution \jour Model. Anal. Inform. Sist. \yr 2016 \vol 23 \issue 3 \pages 370--376 \mathnet{http://mi.mathnet.ru/mais508} \crossref{https://doi.org/10.18255/1818-1015-2016-3-370-376} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520860} \elib{http://elibrary.ru/item.asp?id=26246304}