Global fractional-order projective dynamical systems

• Fractional-order projective dynamical system is investigated for the first time.
• Existence of solutions has been explored and obtained.
• Existence and uniqueness of the equilibrium point have been proved.
• An algorithm for finding solutions has been given and applied.
• A numerical simulation is given to illustrate results obtained in this paper.

This paper studies a class of global fractional-order projective dynamical systems. First, we show the existence and uniqueness of the solution of this type of system. Then, the existence of the equilibrium point of this class of dynamical systems is obtained. Further more, we obtain the α-exponential stability of the equilibrium point under suitable conditions. In addition, we use a predictor–corrector algorithm to find a solution to this kind of system. Finally a numerical example is provided to illustrate the results obtained in this paper.