Hypercyclic and Topologically Mixing Properties of Abstract Time-Fractional Equations With Discrete Shifts
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: alignFDEab1 & D_t^α_n u(t)+ A_n-1 D_t^α_n-1 u(t)+· · · + A_1 D_t^α_1 u(t)= A_0D_t^αu(t), t > 0, otag & u^(k)(0)=u_k, k=0,· · ·, α_n ceil -1. align where nN{1}, A_0,A_1,· · · ,A_n-1 are closed linear operators acting on a separable infinite-dimensional complex Banach space E, 0 ≤ α_1<· · ·<α_n, 0≤ α<α_n, and D_t^α denotes the Caputo fractional derivative of order α (bajlekova), have been recently clarified in hf-icdea. In this paper, we continue the analysis contained in hf-icdea by assuming that, for every jN_n-1, the operator A_j is a certain function of unilateral backward shifts acting on weighted l^1(C)-spaces. 2010 Mathematics Subject Classification. 47A16, 26D33, 47D06. , number=2, journal=Sarajevo Journal of Mathematics, author=Kostić, Marko, year=2024, month=Jun., pages=257–269