On discrete sequential fractional boundary value problems

In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is −Δμ1Δμ2Δμ3y(t)=f(t+μ1+μ2+μ3−1,y(t+μ1+μ2+μ3−1)) subject to the conjugate boundary conditions y(0)=0=y(b+2), where f:[1,b+1]N0×R→[0,+∞) is a continuous function and μ1,μ2,μ3∈(0,1) satisfy 1<μ2+μ3<2 and 1<μ1+μ2+μ3<2. We also obtain results for delta–nabla discrete fractional boundary value problems. As an application of our analysis, we give conditions under which such problems will admit at least one positive solution.