DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE

Marina V. Plekhanova     (Computational Mechanics Department, South Ural State Universit and Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk, Russian Federation)

Abstract


The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential 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 dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid

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DOI: http://dx.doi.org/10.15826/umj.2016.2.006

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