Existence and Uniqueness of Solutions to Abstract Discrete-Time Cauchy Problems in Vector-Valued Weighted Spaces

This article studies the abstract discrete-time Cauchy problem involving the Riemann-Liouville type difference operator. Sufficient conditions for the existence of unique solution to the semilinear Cauchy problem in Lebesgue and weighted Lebesgue vector-valued spaces are shown. Finally, some examples are presented to illustrate the main results.