@Article{Idczak2016,
author = "Idczak, Dariusz and Walczak, Stanislaw",
title = "On a linear-quadratic problem with Caputo derivative",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "1",
pages = "49--68",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.1.49",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.1.49",
abstract = "In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.",
keywords = "fractional Caputo derivative, linear-quadratic problem, existence and uniqueness of a solution, maximum principle, gradient method, projection of the gradient method",
issn = "1232-9274"
}