The paper studies a fractional-order differential inclusion of the form
subject to two classes of boundary conditions
(1) , ;
(2) , .
is a set-valued map, denotes the Caputo fractional derivative of order , , , and , .
Three existence results are obtained for the problems considered. The first result relies on the nonlinear alternative of Leray-Schauder type, the second result essentially uses the Bressan-Colombo selection theorem for lower semicontinuous set-valued maps with decomposable values and the third result is based on the Covitz-Nadler contraction principle for set-valued maps.