Start control problem for a class of degenerate equations with lower order fractional derivatives. (Russian. English summary) Zbl 1470.49008

Baĭbulatova, G. D.

Chelyabinskiĭ Fiz.-Mat. Zh. 5, No. 3, 271-284 (2020).

Summary: Fractional order degenerate evolution equation with lower fractional derivatives is studied. The case of a relatively bounded pair of operators in the main part of the equation is considered. For linear and semilinear equations the existence of a unique strong solution of the generalized Showalter-Sidorov problem is proved. These results are used for the proof of the solvability of the start control problem in the linear and the semilinera case. The obtained results are applied to study of an optimal control problem for a fractional order in time degenerate distributed system.

MSC:

49J20	Existence theories for optimal control problems involving partial differential equations
34A08	Fractional ordinary differential equations

Keywords:

fractional derivative; degenerate evolution equation; nonlinear differential equation; start control

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