On linear conflict-controlled processes with fractional derivatives

A control problem is considered for quasilinear processes with fractional derivatives under counteraction. Hilfer fractional derivatives are studied, which, in particular, include the classical Riemann–Liouville fractional derivatives and Caputo regularized derivatives. A representation for solutions of such systems is presented, which allows to obtain, using the method of resolving functions, a guaranteed result for the approach of a trajectory to a given target set. Qualitative results are illustrated by an example with the Bagley–Torvik equation, which describes damped oscillations with fractional damping, and by a game problem with the equation of fractional relaxation.