Fractional nonlinear dynamics of DNA breathing

The classical Lagrangian formulation for the nonlinear dynamics of a homogeneous Peyrard-Bishop DNA molecular chain is reviewed and extended to include coordinates with time derivative of fractional order γ (0 < 2γ < 2), which can be viewed as memory effect. We obtain the equations of motion depending on γ. The analytical procedure for obtaining nonlinear waves solutions is performed through the application of a powerful fractional perturbation technique. The results show that both the amplitude and the velocity of waves increase when γ decreases. Accordingly, for low values of γ, the system exhibits highly localized waves with high amplitude and velocity. The numerical results agree with the theoretical ones and show that the system can support fractional breather-like modes.