  We develop the Benkhettou-Hassani-Torres fractional (noninteger order)
calculus on time scales by proving two chain rules for the $\alpha$-fractional
derivative and five inequalities for the $\alpha$-fractional integral. The
results coincide with well-known classical results when the operators are of
(integer) order $\alpha = 1$ and the time scale coincides with the set of real
numbers.
