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In this paper, we discussed the existence of solutions for the fractional finite difference inclusion $\Delta^{\nu}x(t)\in F(t,x(t),\Delta x(t),\Delta^{2} x(t))$ via the boundary value conditions $\xi x(\nu-3)+\beta\Delta x(\nu -3)=0$, $x(\eta)=0$, and $\gamma x(b+\nu)+\delta\Delta x(b+\nu)=0$, where $\eta\in\mathbb{N}_{\nu-2}^{b+\nu-1}$, $2<\nu<3$, and $F:\mathbb {N}_{\nu-3}^{b+\nu+1}\times\mathbb{R}\times\mathbb{R}\times\mathbb {R}\to2^{\mathbb{R}} $ is a compact valued multifunction. [ABSTRACT FROM AUTHOR]

We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results. [ABSTRACT FROM AUTHOR]

In this manuscript we investigated the fractional finite difference inclusion Δμμ-2x(t) ϵ F(t, x(t), Δx(t)) via the boundary conditions Δx(b + μ) = A and x(μ - 2) = B, where 1 < μ ≥ 2, A, B ϵ R and F : Nb+μ+2μ-2 × R × R → 2R is a compact valued multifunction. [ABSTRACT FROM AUTHOR]

Recently, the existence of solution for the fractional self-adjoint equation Δν-1ν(pΔy)(t) = h(t) for order 0 < ν ≤ 1 was reported in [9]. In thispaper, we investigated the self-adjoint fractional finite difference equation Δν-2ν(pΔy)(t) = h(t,p(t + ν -- 2)Δy(t + ν -- 2)) via the boundary conditions y(ν -- 2) = 0, such that Δy (ν -- 2) = 0 and Δy(ν + b) = 0. Also, we analyzed the self-adjoint fractional finite difference equation Δν-2ν(pΔ²y)(t) = h(t,p(t + ν -- 3)Δ²y(t + ν -- 3)) via the boundary conditions y(ν -- 2) = 0, Δy(ν -- 2) = 0, Δ²y(ν -- 2) = 0 and Δ²y(ν + b) = 0. Finally, we conclude a result about the existence of solution for the general equation Δν-2937(pΔmy)(t) = h(t,p(t + ν -- m -- 1)Δmy(t + ν -- m -- 1)) via the boundary conditions y(ν -- 2) = Δy(ν -- 2) = Δ²y(ν -- 2) = ... = Δmy(ν -- 2) = 0 and Δmy(ν + b) = 0 for order 1 < ν ≤ 2. [ABSTRACT FROM AUTHOR]