Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives.

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 C 1 ([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the a u g m e n t e d -RBF method. Several examples illustrate the good performance of the numerical method. [ABSTRACT FROM AUTHOR]