  This paper provides a probabilistic approach to solve linear equations
involving Caputo and Riemann-Liouville type derivatives. Using the
probabilistic interpretation of these operators as the generators of
interrupted Feller processes, we obtain well-posedness results and explicit
solutions (in terms of the transition densities of the underlying stochastic
processes). The problems studied here include fractional linear differential
equations, well analyzed in the literature, as well as their far reaching
extensions.
