Stabilization of unstable trajectories in discrete and continuous fractional order dynamical systems

A novel technique that is used to stabilize unstable trajectories in nonlinear dynamical systems is presented. The con-structed technique depends on specific choice of initial conditions which is achieved by employing the notion of H-rank for the algebraic complexity evaluation of transient processes. The efficacy of the presented stabilization technique is shown for the frac-tional difference logistic map as well as driven fractional nonlinear pendulum dissipation.