Fractional dynamical system and its linearization theorem

By Changpin Li, Yutian Ma. 2013

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Stability analysis for nonlinear fractional-order systems based on comparison principle (2014, background): “However, there are few results concerning how to directly analyze and control nonlinear fractionalorder systems except for linearization [30, 31].”
On explicit stability conditions for a linear fractional difference system (2015, methodology): “Based on linearization method for fractional differential equations (see [16]), local stability investigations along x∗ can be reduced to analysis of the linear system Dx1(t) = x2(t), Dx2(t) = −kx1(t)− cx2(t).”
Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems (2015, background): “Figure 1 shows the changes in treach alongwith λ and β̄, in which λ ∈ [2, 6] and β̄ ∈ [0, 0.”