Well-posedness and qualitative properties for abstract time-difference equations
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Díaz Noguera, Stiven E.
In this thesis we introduce the notions of the stable Levy process and the scaled Wright function within the discrete setting. Using these notions, we prove a subordination principle which will be used to investigate different classes of discrete time fractional difference equations. In addition, we introduce the Banach space of (N, λ)-periodic vector-valued sequences. Moreover, we show the existence and uniqueness of (N, λ)-periodic solutions to a class of abstract Volterra difference equations as well as of fractional difference equations.