Geodesic
Degenerate distributed control systems with fractional time derivative
Ural mathematical journal, Tome 2 (2016) no. 2, pp. 58-71

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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, Degenerate evolution equation, (L,p)-bounded operator, Optimal control, Fractional viscoelastic fluid.
Mots-clés : Partial differentialequation 
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     title = {Degenerate distributed control systems with fractional time derivative},
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Marina V. Plekhanova. Degenerate distributed control systems with fractional time derivative. Ural mathematical journal, Tome 2 (2016) no. 2, pp. 58-71. http://geodesic.mathdoc.fr/item/UMJ_2016_2_2_a5/