New Dynamic Multiwave Solutions of the Fractional Peyrard–Bishop DNA Model

Abstract

In this paper, we have studied the new solitary wave solutions of the beta-fractional derivative form of the Peyrard–Bishop DNA model (PB-DNAM). These solutions are responsible for analyzing the nonlinear interaction between the adjacent displacements of the DNA strand. To get these solutions, we have applied the generalized Riccati equation expansion method. Under different parametric conditions and fractional values, the obtained solutions show different wave patterns including w-shape, bright, combined dark-bright, periodic wave solutions, bell shape, m-shape, w-shape along with two bright solutions, and m-shape along with two dark solutions. These physical characteristics are analyzed thoroughly by graphical representations. The solutions show the successful application of the proposed method which will be helpful in finding analytical solutions to other nonlinear problems.