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**Mixed control for linear infinite-dimensional systems of fractional order.**
*(Russian.
English summary)*
Zbl 1471.93148

Summary: Problem with a mixed control, start and distributed simultaneously, are considered for time-fractional order evolution equations. The results on the solvability of the mixed control problems for linear non-degenerate and degenerate equations with the Gerasimov-Caputo fractional derivative are obtained. It is shown that at some additional conditions a solution of the considered problem is unique. General results are used for consideration of abstract problems with specific quality functionals. Abstract results of the work are illustrated by the example of a mixed control problem for the time-fractional order system of gravitational-gyroscopic waves.

### MSC:

93C35 | Multivariable systems, multidimensional control systems |

93C05 | Linear systems in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

26A33 | Fractional derivatives and integrals |

### Keywords:

optimal control; mixed control; fractional order equation; Gerasimov-Caputo derivative; degenerate evolution equation
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\textit{M. V. Plekhanova} and \textit{A. F. Shuklina}, Chelyabinskiĭ Fiz.-Mat. Zh. 5, No. 1, 32--43 (2020; Zbl 1471.93148)

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