Geodesic
A Caputo two-point boundary value problem: existence, uniqueness and regularity of a solution
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 370-376

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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, uniqueness, regularity.
Mots-clés : existence 
@article{MAIS_2016_23_3_a14,
     author = {M. Stynes},
     title = {A {Caputo} two-point boundary value problem: existence, uniqueness and regularity of a solution},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {370--376},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a14/}
}
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M. Stynes. A Caputo two-point boundary value problem: existence, uniqueness and regularity of a solution. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 370-376. http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a14/