The Cauchy Problem For Discrete Time Fractional Evolution Equations

This paper is devoted to the study of discrete-time fractional evolution equations involving the Riemann–Liouville-like difference operator. Based on the relationship between C₀-semigroups and a distinguished class of sequences of operators, we show the structure of the solutions for the inhomogeneous Cauchy problem of abstract fractional difference equations. Further, we establish two criteria for the existence and uniqueness of solutions for the semilinear Cauchy problem. Some examples are also provided to illustrate our main results.