Aurelian Cernea
University of Bucharest, Bucharest, Romania

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