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Stability Analysis for Discrete Time Abstract Fractional Differential Equations

In this paper, we consider a discrete-time fractional model of abstract form involving the Riemann-Liouville-like difference operator. On account of the C 0 -semigroups generated by a closed linear operator A and based on a distinguished class of sequences of operators, we show the existence of stable solutions for the nonlinear Cauchy problem by means of fixed point technique and the compact method. Moreover, we also establish the Ulam-Hyers-Rassias stability of the proposed problem. Two examples are presented to explain the main results.