Abstract
In this paper, we introduce several existence theorems for a discrete fractional boundary value problem with Dirichlet boundary conditions in the case where the order ν of the fractional difference satisfies 1 < ν ≤ 2. We use cone theoretic techniques to deduce the existence of one or more positive solutions. We then deduce uniqueness theorems for the same problem by assuming a Lipschitz condition. We show that many of the classical existence and uniqueness theorems for second-order discrete boundary value problems extend to the fractional-order case.
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