Existence of (N,λ ) -Periodic Solutions for Abstract Fractional Difference Equations

We establish sufficient conditions for the existence and uniqueness of (N,λ ) -periodic solutions for the following abstract model: Δ ^αu(n)=Au(n+1)+f(n,u(n)), n∈ℤ, where 0 < α≤ 1 , A is a closed linear operator defined in a Banach space X , Δ ^α denotes the fractional difference operator in the Weyl-like sense, and f satisfies appropriate conditions.