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 Fractional boundary value problem with nabla difference equation Qiaoluan Li,Yani Liu,Lina Zhou Keywords:Fractional difference equation; Existence; Eigenvalue Abstract: In the paper, using Z-transform technique, we study eigenvalues and eigenfunctions for a fractional boundary value problem with linear nabla difference equation. Furthermore, by topological degree theory and the obtained results of eigenvalues, we get at least one nontrivial solution for relevant nonlinear fractional boundary value problem.