LAUSR

Abstract The approximate controllability of a class of infinite dimensional control systems, described by the equation not solved with respect to the fractional Caputo derivative, is studied. Under the supposition of relative p-boundedness of the pair of operators in the equation the control system is reduced to two subsystems on mutually complement subspaces. One of subsystem is solved with respect to the fractional derivative, another subsystem has a nilpotent operator at the derivative. It is proved the equivalence of the approximate controllability of the original system and of every of two subsystems by the same control. This fact applied to the deriving of a criterion of the approximate controllability of the degenerate control system after research of every subsystem approximate controllability conditions. Application of the criterion is demonstrated on an example of a system described by partial differential equations.