On approximate controllability of a class of degenerate fractional order distributed systems

Abstract

The approximate controllability issues for a class of control systems, whose dynamics is described by an equation in a Banach space with a linear degenerate operator at the Riemann — Liouville fractional derivative, is investigated. Under the condition of p-boundedness of the pair of operators in the equation the control system is reduced to subsystems on two mutually complement subspaces. It was shown that the approximate controllability of the whole system is equivalent to the approximate controllability of the two subsystems. Criteria of the approximate controllability for the system and two subsystems are obtained. Analogous results are got on the approximate controllability for free time and for systems of the same form with a finite-dimensional input. The obtained criteria were applied to the investigation of the approximate controllability for a distributed system with polynomials of a differential with respect to the spatial variables self-adjoint elliptic operator and for a system of the Scott-Blair — Oskolkov type.