Abstract
In Hilbert space, the finite-dimensional exact controllability of an abstract semilinear fractional composite relaxation equation is researched. We make assumptions about the parameters in the equation and suppose that the linear equation associated with the abstract semilinear fractional relaxation equation is approximately controllable. We apply the variational method, the resolvent theory and the fixed point trick to demonstrate the finite-dimensional exact controllability of the abstract semilinear equation. An application is given in the last paper to testify our results.
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