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We consider a discrete fractional nonlinear boundary value problem in which nonlinear term f  is involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions

Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference