Abstract
A two-point boundary value problem whose highest-order term is a Riemann-Liouville fractional derivative of order δ ∈ (1, 2) is considered on the interval [0, 1]. It is shown that the solution u of the problem lies in C[0, 1] but not in C 1[0, 1] because u′(x) blows up at x → 0 for each fixed value of δ. Furthermore, u′(1) blows up as δ → 1+ if and only if the constant convection coefficient b satisfies b ≥ 1.
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Acknowledgements
This paper was written while the second author was visiting the University of Zaragoza, supported by the Institute of Mathematics and Applications (IUMA). The research was also partly supported by the projects MTM2013-40842-P, UZCUD2014-CIE-09 and the Diputación General de Aragón.
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Gracia, J.L., Stynes, M. (2015). Boundary Layers in a Riemann-Liouville Fractional Derivative Two-Point Boundary Value Problem. In: Knobloch, P. (eds) Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-25727-3_7
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DOI: https://doi.org/10.1007/978-3-319-25727-3_7
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