Investigating the DNA Peyrard–Bishop model by beta derivatives using new analytical technique

The aim of this study is to extract some analytical solutions of the Peyrard–Bishop deoxyribonucleic acid ([Formula: see text]-PBDNA) dynamic model with [Formula: see text]-derivatives of the novel modified ([Formula: see text]-expansion method. In addition, we study the effect of various parameters of the fractional model on soliton dynamics. This research focuses on computational biophysics and data science, which studies the effects of various parameters on fractional structures. This paper contributes to the understanding of the solution and [Formula: see text]-PBDNA dynamic model by showing the applicability of the novel modified ([Formula: see text]-expansion method for many fractional models. The implementation of the scheme successfully completed some solutions of the model. Following the novel modified ([Formula: see text]-expansion method, we use fractional transform to transform the model into a nonlinear differential equation. In this way, a linear equation system is formed. After the solution, the soliton solution of the appropriate process is obtained. We also compare our obtained solutions with the existing solutions in the literature in Table 1, which shows the novelty of our work. Also, this paper presents 3D, 2D and contour plots of various solutions at appropriate parameter values. The results contribute to the interpretation of the model in future studies and confirm that the novel modified ([Formula: see text]-expansion method is effective for a wide range of model fractions, including analyzing the plots to show the difference between these solutions.