Weighted Pseudo Almost Automorphic and S-asymptotically Ω-periodic Solutions to Fractional Difference-differential Equations
نویسندگان
چکیده
We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation ∆u(n) = Au(n+ 1) + f(n, u(n)), n ∈ Z, for 0 < α ≤ 1, whereA is the generator of an α-resolvent sequence {Sα(n)}n∈N0 in B(X). We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(·, ·) is weighted almost automorphic in the first variable and satisfies a Lipschitz (local and global) type condition in the second variable. An analogous result is also proved for S-asymptotically ω-periodic solutions.
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