Abstract
In this paper, we investigate the solutions set for a q-fractional differential inclusion
(1.1) D-c(q)alpha x(t) is an element of F t, x(t),(c) D-q(alpha) x(t), t is an element of [0, T],
with the initial condition
(1.2) x (0) = x(0)
where q is an element of (0; 1) and alpha is an element of (0, 1], T > 0, F : [0, T] x R x R -> P (R) is a multi-valued map.
Our result is based on the fixed point theorem for multi-valued maps due to Covitz and Nadler. We also establish some Filippov's-type results for the problem (1.1)-(1.2). Finally, an example is presented to illustrate our main results.