On a fractional boundary value problem with fractional boundary conditions

In this paper, we consider a discrete fractional boundary value problem, for t∈[0,b+1]N0t∈[0,b+1]N0, of the form −Δνy(t)=f(t+ν−1,y(t+ν−1))−Δνy(t)=f(t+ν−1,y(t+ν−1)), y(ν−2)=0y(ν−2)=0, [Δαy(t)]t=ν+b−α+1=0[Δαy(t)]t=ν+b−α+1=0, where f:[ν−1,…,ν+b]Nν−2×R→Rf:[ν−1,…,ν+b]Nν−2×R→R is continuous, 1<ν≤21<ν≤2, and 0≤α<10≤α<1. We prove that this problem can be interpreted as a discrete multipoint problem. We also show that the problem is a generalization of some recent results. Our results provide some basic analysis of discrete fractional boundary conditions.