  We consider the discrete, fractional operator $\left(L_a^\nu x\right) (t) :=
\nabla [p(t) \nabla_{a^*}^\nu x(t)] + q(t) x(t-1)$ involving the nabla Caputo
fractional difference, which can be thought of as an analogue to the
self-adjoint differential operator. We show that solutions to difference
equations involving this operator have expected properties, such as the form of
solutions to homogeneous and nonhomogeneous equations. We also give a variation
of constants formula via a Cauchy function in order to solve initial value
problems involving $L_a^\nu$. We also consider boundary value problems of any
fractional order involving $L_a^\nu$. We solve these BVPs by giving a
definition of a Green's function along with a corresponding Green's Theorem.
Finally, we consider a (2,1) conjugate BVP as a special case of the more
general Green's function definition.
