Generation of nonlocal fractional dynamical systems by fractional differential equations. (English) Zbl 1385.34009

Cong, N. D.; Tuan, H. T.

J. Integral Equations Appl. 29, No. 4, 585-608 (2017).

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

Keywords:

fractional differential equations; dynamical system; two parameter flow; initial value problem; nonlocal boundary problem; growth and boundedness