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\(\mathcal D\)-hypercyclic and \(\mathcal D\)-topologically mixing properties of degenerate multi-term fractional differential equations. (English) Zbl 1329.47008

Summary: In the paper under review, we introduce the notions of \(\mathcal{D}\)-hypercyclicity and \(\mathcal{D}\)-topologically mixing property of degenerate abstract multi-term fractional differential equations with Caputo fractional derivatives. The obtained results are illustrated with some examples.

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators
47D06 One-parameter semigroups and linear evolution equations
47G20 Integro-differential operators
34G10 Linear differential equations in abstract spaces
34A08 Fractional ordinary differential equations
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