In the study of dynamical systems given by differential equations of fractional order, due to difficulty of determining derivative operator, more efforts are focused on numerical modeling of the limiting dynamics of such systems. At the same time, the questions whether the system of differential equations of fractional order actually generates a dynamic system (i.e. whether it is possible to extend the solutions of a system for an interval $[0, +\infty]$) and, also whether there are in phase space of such systems attractors (i.e. invariant, limited, attracting sets) usually remain open. These questions, in particular, are connected with property of dissipativity in the sense of Levinson (or D-property), when in phase space there is a bounded absorbing set, inside which at some point all system trajectories fall and no longer leave. Thus, if a system of differential equations is dissipative in this sense: first, it produces a dynamic system, and second, it contains a global attractor within the absorbing set.