Right Fractional Sobolev Space via Riemann-Liouville Derivatives on Time Scales and an Application to Fractional Boundary Value Problem on Time Scales

Using the concept of fractional derivatives of Riemann-Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain their completeness, reflexivity, separability and some embeddings. Finally, as an application, we propose a recent method to study the existence of weak solutions of fractional boundary value problems on time scales by using variational methods and critical point theory, and, by constructing an appropriate variational setting, we obtain two existence results of the problem.