In this paper, we investigate the existence of solutions for a class of fractional $q$--difference inclusions with anti-periodic boundary value conditions with $\uppsi$-Caupto fractional $q$--derivative. By means of some standard nonlinear theorems, sufficient conditions for the existence of solutions for the fractional $q$-differential inclusions under $\uppsi$-Caputo $q$--derivatives are presented where the real function $\uppsi$ is increasing. Our result generalizes the known special case if $\uppsi(t) = t$ and single known results to the multi-valued ones.
