In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.P.A. is partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific projects PEstOE/MAT/UI0208/2013 and PTDC/MAT-CAL/4334/2014. R.F. was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.info:eu-repo/semantics/publishedVersio
