  In this paper, a finite-horizon optimal control problem involving a dynamical
system described by a linear Caputo fractional differential equation and a
quadratic cost functional is considered. An explicit formula for the value
functional is given, which includes a solution of a certain Fredholm integral
equation. A step-by-step feedback control procedure for constructing
$\varepsilon$-optimal controls with any accuracy $\varepsilon > 0$ is proposed.
The basis for obtaining these results is the study of a solution of the
associated Hamilton-Jacobi-Bellman equation with so-called fractional
coinvariant derivatives.

Optimization and Control