56087 20210121114458.0 doi 10.1515/cmam-2014-0024 sideral 89299 ART-2015-89299 eng Stynes, M. Boundary layers in a two-point boundary value problem with a caputo fractional derivative 2015 Access copy available to the general public Unrestricted A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Caputo fractional derivative of order ¿ with 1 < ¿ < 2. Writing ¿ for the solution of the problem, it is known that typically ¿¿¿(¿) blows up as ¿ ¿ 0. A numerical example demonstrates the possibility of a further phenomenon that imposes difficulties on numerical methods: ¿ may exhibit a boundary layer at ¿ = 1 when ¿ is near 1. The conditions on the data of the problem under which this layer appears are investigated by first solving the constant-coefficient case using Laplace transforms, determining precisely when a layer is present in this special case, then using this information to enlighten our examination of the general variable-coefficient case (in particular, in the construction of a barrier function for ¿). This analysis proves that usually no boundary layer can occur in the solution ¿ at ¿ = 0, and that the quantity ¿ = max¿¿[0,1] ¿(¿), where ¿ is the coefficient of the first-order term in the differential operator, is critical: when¿ < 1,noboundarylayerispresentwhen¿isnear1,butwhen¿ = 1thenaboundarylayerat¿ = 1 is possible. Numerical results illustrate the sharpness of most of our results. info:eu-repo/grantAgreement/ES/MEC/MTM2010-16917 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 0.673 2015 MATHEMATICS, APPLIED 163 / 254 = 0.642 2015 Q3 T2 0.901 2015 Applied Mathematics 2015 Q2 Numerical Analysis 2015 Q2 Computational Mathematics 2015 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion (orcid)0000-0003-2538-9027 Gracia, J.L. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 15, 1 (2015), 79-95 Comput. methods appl. math. Computational Methods in Applied Mathematics 1609-4840 687666 http://zaguan.unizar.es/record/56087/files/texto_completo.pdf Versión publicada 85645 http://zaguan.unizar.es/record/56087/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:56087 articulos driver 2021-01-21-10:49:46 ARTICLE