DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE
Copyright policy )DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE
Summary: 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.
- Chelyabinsk State University Russian Federation
- South Ural State University Russian Federation
- FEDERAL STATE AUTONOMOUS EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION NOTHERN (ARCTIC) FEDERAL UNIVERSITY Russian Federation
FRACTIONAL VISCOELASTIC FLUID, degenerate evolution equation, CAPUTO DEIVATIVE, \((L,p)\)-bounded operator, Fractional dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid, fractional differential calculus, Existence theories for optimal control problems involving partial differential equations, PDEs in connection with fluid mechanics, DEGENERATE EVOLUTION EQUATION, Fractional partial differential equations, Caputo derivative, optimal control, OPTIMAL CONTROL, partial differentialequation, Mittag-Leffer function, FRACTIONAL DIERENTIAL CALCULUS, QA1-939, Optimality conditions for problems involving partial differential equations, fractional viscoelastic fluid, Viscoelastic fluids, PARTIAL DIERENTIAL EQUATION, Mathematics, MITTAG-LEER FUNCTION
FRACTIONAL VISCOELASTIC FLUID, degenerate evolution equation, CAPUTO DEIVATIVE, \((L,p)\)-bounded operator, Fractional dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid, fractional differential calculus, Existence theories for optimal control problems involving partial differential equations, PDEs in connection with fluid mechanics, DEGENERATE EVOLUTION EQUATION, Fractional partial differential equations, Caputo derivative, optimal control, OPTIMAL CONTROL, partial differentialequation, Mittag-Leffer function, FRACTIONAL DIERENTIAL CALCULUS, QA1-939, Optimality conditions for problems involving partial differential equations, fractional viscoelastic fluid, Viscoelastic fluids, PARTIAL DIERENTIAL EQUATION, Mathematics, MITTAG-LEER FUNCTION
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