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It is supposed that the fractional difference equation  Open image in new window ,  Open image in new window  has an equilibrium point  Open image in new window  and is exposed to additive stochastic perturbations type of  Open image in new window  that are directly proportional to the deviation of the system state  Open image in new window  from the equilibrium point  Open image in new window . It is shown that known results in the theory of stability of stochastic difference equations that were obtained via V. Kolmanovskii and L. Shaikhet general method of Lyapunov functionals construction can be successfully used for getting of sufficient conditions for stability in probability of equilibrium points of the considered stochastic fractional difference equation. Numerous graphical illustrations of stability regions and trajectories of solutions are plotted.

Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations