A Darboux problem associated to a fractional hyperbolic integro-differential inclusion defined by a Caputo type fractional derivative is studied. We obtain an existence result for this problem in the situation when the values of the set-valued map are not convex by employing a method originally introduced by Filippov. Also, we provide the existence of solutions continuously depending on a parameter for the problem studied. This second result allows to deduce a continuous selection of the solution set of the problem considered.