Chain rules and inequalities for the BHT fractional calculus on arbitrary time scales

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.