  We first prove the equivalence of two definitions of Riemann-Liouville
fractional integral on time scales, then by the concept of fractional
derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev
spaces, characterize them, define weak fractional derivatives, and show that
they coincide with the Riemann-Liouville ones on time scales. Next, we prove
equivalence of some norms in the introduced spaces and derive their
completeness, reflexivity, separability and some imbeddings. Finally, as an
application, by constructing an appropriate variational setting, using the
mountain pass theorem and the genus properties, the existence of weak solutions
for a class of Kirchhoff-type fractional p-Laplacian systems on time scales
with boundary condition is studied, and three results of the existence of weak
solutions for this problem is obtained.
