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Abstract
We study the boundary controllability of fractional wave (also known as super diffusion) equations associated to the Caputo fractional derivative with a symmetric non-negative uniformly elliptic operator subject to the non-homogeneous Dirichlet- or Robin-type boundary conditions. Our results show that if and
is a connected bounded open set with smooth boundary
, then the system
in
,
on
,
,
, is approximately controllable for any
,
,
any non-empty open set and any
, where
in the case of the Dirichlet boundary condition and
for the Robin boundary conditions. Here
denotes the dual of the domain of the fractional power of order
of the realization in
of the operator A with the zero boundary conditions
on
. The results obtained in the article are optimal given that such a system cannot be null controllable.
Acknowledgements
We would like to thank the referee for the careful reading of the manuscript and for his helpful comments and suggestions.
Notes
No potential conflict of interest was reported by the author.