Investigation of soliton solutions to the Peyrard-Bishop-Deoxyribo-Nucleic-Acid dynamic model with beta-derivative

Abstract

This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid (beta-PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the beta-PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions.