Nabla fractional calculus on time scales

In this thesis, the properties of the Nabla fractional derivative and fractional integral in the case of Riemann-Liouville on the time scale are investigated. Moreover, the Nabla fractional derivative is also introduced in the case of Grünwald-Letnikov. On the other hand, the Sturm-Liouville problem via the Nabla Riemann-Liouville fractional derivative and its properties are investigated on an arbitrary time scale. For this problem, spectral properties such as Lagrange identity, Green's formula, Abel's formula, self-adjointness and orthogonality of eigenfunctions in terms of Nabla RiemannLiouville fractional derivative are expressed on an arbitrary time scale.