Controllability of nonlinear fractional evolution systems in Banach spaces: a survey. (English) Zbl 1478.93070
In this paper, authors have presented a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal initial conditions, FESs with a time delay or impulsive effects. Furthermore, controllability results via resolvent operator are reviewed in details. Finally, the conclusions of this work and the research prospect are presented, which provides a reference for further studies.
Reviewer: Yong-Kui Chang (Xi’an)
MSC:
| 93B05 | Controllability |
| 93C25 | Control/observation systems in abstract spaces |
| 34K30 | Functional-differential equations in abstract spaces |
| 35R11 | Fractional partial differential equations |
| 37L05 | General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations |
Keywords:
controllability; fractional evolution systems; mild solutions; impulse; time delay; fixed point theoremReferences:
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