Nontrivial solutions for a nonlinear th order atici-eloe fractional difference equation satisfying dirichlet boundary conditions

For 1 < nu <= 2 a real number and T >= 2 a natural number, by an application of a Krasnosel'skii-Zabreiko fixed point theorem, nontrivial solutions are established for a nonlinear nu th order Atici-Eloe fractional difference equation, Delta(nu)u(t) + f(u(t + nu - 1)) = 0, t is an element of {1,2, ... , T + 1}, satisfying the Dirichlet boundary conditions u(nu - 2) = u(nu + T + 1) = 0, where f : R -> R is continuous and lim(vertical bar r vertical bar ->infinity) f(r)/r exists.