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: Δαu(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. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.