Abstract
The dynamics of nonlinear system is very complicated
especially the fractional nonlinear system since they can be
found in many areas of engineering and science. The
dynamics of the Lorenz system with fractional derivatives is
analysed based on the frequency approximation. For a given
range of parameters where the non‐fractional Lorenz system
has periodic orbits, it is found that the fractional Lorenz
system exhibits chaos and hyperchaos. A striking finding is
that the fractional Lorenz system exhibits hyperchaos,
although the total system order is less than 3, which is
contrary to the well known conclusion that hyperchaos
cannot occur in the integer‐order continuous‐time
autonomous system of order less than 4. Finally, a
reasonable explanation is offered for this complicated
dynamical phenomenon.