Features of the phase dynamics of fractional two-dimensional linear control systems for various differentiation operator

This paper is devoted to the study of the phase dynamics of fractional linear systems with control. Two-dimensional systems with concentrated parameters are considered in most detail in the cases where the fractional differentiation operators in the governing equations are understood in the Caputo–Fabrizio sense. Systems modeled by equations with Atangana–Baleano and Prabhakara operators are also considered. We obtain and examine analytic solutions and boundary trajectories of systems, which determine domains of admissible values of the phase coordinates. The statement of the moment $l$-problem for the systems considered and its solvability are analyzed. An example of solving this problem in the case where the control is an essentially bounded function on a interval is given.