Can We Obtain a Fractional Lorenz System from a Physical Problem?

A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension Σ, we find a critical value of the effective dimension Σ_cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value Σ_cr2 (Σ_cr2 <Σ_cr1)at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of Σ is found to delay the onset of it.