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The most valuable theoretical results about hypercyclic and topologically mixing properties of some special subclasses of the abstract time-fractional equations of the following form: Dn t u(t) +An−1D αn−1 t u(t) + · · ·+A1D α1 t u(t) = A0D α t u(t), t > 0, u(0) = uk, k = 0, · · ·, dαne − 1. (1) where n ∈ N \ {1}, A0, A1, · · ·, An−1 are closed linear operators acting on a separable infinite-dimensional complex Banach space E, 0 ≤ α1 < · · · < αn, 0 ≤ α < αn, and Dt denotes the Caputo fractional derivative of order α ([1]), have been recently clarified in [12]-[13]. In this paper, we continue the analysis contained in [12]-[13] by assuming that, for every j ∈ Nn−1, the operator Aj is a certain function of unilateral backward shifts acting on weighted l(C)-spaces.

Hypercyclic and topologically mixing properties of abstract timefractional equations with discrete shifts