Geodesic
Mixed control for linear infinite-dimensional systems of fractional order
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 32-43

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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.
Keywords: optimal control, mixed control, fractional order equation, Gerasimov — Caputo derivative, degenerate evolution equation. 
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     author = {M. V. Plekhanova and A. F. Shuklina},
     title = {Mixed control for linear infinite-dimensional systems of fractional order},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {32--43},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a2/}
}
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M. V. Plekhanova; A. F. Shuklina. Mixed control for linear infinite-dimensional systems of fractional order. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 32-43. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a2/