This article is cited in 8 papers

Degenerate distributed control systems with fractional time derivative

Marina V. Plekhanova<sup>ab

a</sup> Computational Mechanics Department, South Ural State University, Chelyabinsk, Russia
^b Laboratory of Quantum Topology, Mathematical Analysis Department, Chelyabinsk State University, Chelyabinsk, Russia

Abstract: The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional dierential equation and for the generalized Showalter - Sidorov problem to semilinear fractional dierential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal control problems to a system described by the degenerate semilinear fractional evolution equation. Abstract results are applied to the research of an optimal control problem solvability for the equations system of Kelvin-Voigt fractional viscoelastic fluids.

Keywords: Fractional differential calculus, Caputo deivative, Mittag-Leffer function, Partial differentialequation, Degenerate evolution equation, (L,p)-bounded operator, Optimal control, Fractional viscoelastic fluid.

Language: English

DOI: 10.15826/umj.2016.2.006

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