On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points
Rafał Kamocki Marek Majewski
Discrete & Continuous Dynamical Systems - B 2014, 19(8): 2557-2568 doi: 10.3934/dcdsb.2014.19.2557
In the paper we consider a Dirichlet problem for a fractional differential equation. The main goal is to prove an existence and continuous dependence of solution on functional parameter $u$ for the above problem. To prove it we use a variational method.
keywords: continuous dependence Kuratowski-Painlevé limit. Fractional dirichlet problem variational methods saddle points Riemann-Liouville derivative
Existence of optimal solutions to lagrange problem for a fractional nonlinear control system with riemann-liouville derivative
Dariusz Idczak Rafał Kamocki
Mathematical Control & Related Fields 2017, 7(3): 449-464 doi: 10.3934/mcrf.2017016

In the paper, a nonlinear control system containing the Riemann-Liouville derivative of order $α∈(0, 1)$ with a nonlinear integral performance index is studied. We discuss the existence of optimal solutions to such problem under some convexity assumption. Our study relies on the implicit function theorem for multivalued mappings.

keywords: Riemann-Liouville integrals and derivatives fractional control systems existence of optimal solutions

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