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. In contrary, 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, in general, not generate a nonlocal dynamical system.

21 pages

References in corpus (1)

• An instability theorem for nonlinear fractional differential systems

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