The first power weighted version of Hardy’s inequality can be rewritten as∫∞0(xα−1∫x01tαf(t)dt)pdx≤[pp−α−1]p∫∞0fp(x)dx,f≥0,p≥1,α<p−1,where the constant C=[pp−α−1]p is sharp. This inequality holds in the reversed direction when 0≤p<1. In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sharp.