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Using the concept of fractional derivatives of Riemann$-$Liouville on timescales, we first introduce right fractional Sobolev spaces and characterizethem. Then, we prove the equivalence of some norms in the introduced spaces,and obtain their completeness, reflexivity, separability and some imbeddings.Finally, as an application, we propose a recent method to study the existenceof weak solutions of fractional boundary value problems on time scales by usingvariational method and critical point theory, and by constructing anappropriate variational setting, we obtain two existence results of theproblem.

fractal and fractional

Right fractional Sobolev space via Riemann$-$Liouville derivatives on  time scales and an application to fractional boundary value problem on time  scales