In this work, we propose a technique to study nonlinear dynamical systems with fractionalorder.
The main idea of this technique is to transform the fractional-order dynamical system
to the integer one based on Jumarie’s modified Riemann–Liouville sense. Many systems in the
interdisciplinary fields could be described by fractional-order nonlinear dynamical systems, such
as viscoelastic systems, dielectric polarization, electrode-electrolyte polarization, heat conduction,
resistance-capacitance-inductance (RLC) interconnect and electromagnetic waves. To deal
with integer order dynamical system it would be much easier in contrast with fractional-order
system. Two systems are considered as examples to illustrate the validity and advantages of this
technique. We have calculated the Lyapunov exponents of these examples before and after the
transformation and obtained the same conclusions. We used the integer version of our example
to compute numerically the values of the fractional-order and the system parameters at which
chaotic and hyperchaotic behaviors exist.