Geodesic
Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 80-88

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In this paper, we consider a class of start control problems for systems whose states are described by equations in Banach spaces that are not solvable with respect to the highest Gerasimov–Caputo fractional derivative and depend nonlinearly on lower-order fractional derivatives. A theorem on the existence of an optimal control is obtained. Abstract results are applies to the study of the start control problem for the modified Sobolev equation with a fractional derivative in time.
Keywords: optimal control, start control, fractional differential equation, Gerasimov–Caputo derivative, nonlinear evolution equation, degenerate evolution equation. 
@article{INTO_2023_226_a8,
     author = {M. V. Plekhanova and G. D. Baybulatova},
     title = {Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--88},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a8/}
}
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M. V. Plekhanova; G. D. Baybulatova. Solvability of start control problems for a class of degenerate nonlinear equations with fractional derivatives. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 80-88. http://geodesic.mathdoc.fr/item/INTO_2023_226_a8/