Generation of nonlocal fractional dynamical systems by fractional differential equations

Abstract

We show that any two trajectories of solutions of a one-dimensional fractional differential equation (FDE) either coincide or do not intersect each other. However, in the higher-dimensional case, two different trajectories can meet. Furthermore, one-dimensional FDEs and triangular systems of FDEs generate nonlocal fractional dynamical systems, whereas a higher-dimensional FDE does not, in general, generate a nonlocal dynamical system.