In this paper, we deals with the existence and uniqueness of solutions for discrete fractional order three point boundary value problem (BVP) of the form Δ~vw(s)=-f(s+v-1,w(s+v-1)), w(v-3)=ψ (w),Δw(v-3)=0,w(v+b)=Φ(w), where s ∈ [0,b]_(N_0), f : [v-3, v-2, v-1, ..., v+b]N v-3×R→[0,+∞] is a continuous function Ψ, Φ: c ([v - 3, v + b]N v-3) → R are given functions and Δv a discrete fractional operator with 2 < υ ≤ 3. We prove existence and uniqueness of solutions by the contraction mapping principle and Brouwer theorem and also we conclude with examples to illustrate the results.
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