Generation of nonlocal fractional dynamical systems by fractional differential equations. (English) Zbl 1385.34009
Summary: 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.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
