  The current research of fractional Sturm-Liouville boundary value problems
focuses on the qualitative theory and numerical methods, and much progress has
been recently achieved in both directions. The objective of this paper is to
explore a different route, namely, construction of explicit asymptotic
approximations for the solutions. As a study case, we consider a problem with
left and right Riemann-Liouville derivatives, for which our analysis yields
asymptotically sharp estimates for the sequence of eigenvalues and
eigenfunctions.
