Abstract
In this paper, we present a work on dynamic equation of Deoxyribonucleic acid (DNA) derived from the Peyrard–Bishop (PB) model oscillator chain for various dynamical solitary wave solutions. In order to construct novel soliton solutions in the DNA dynamic PB model with beta-derivative, the efficiency of the newly developed algorithms is being investigated, which could include a new auxiliary equation strategy (NAES). Some precise soliton solutions comprising dark, light and other forms of multi-wave soliton solutions are achieved via the proposed methods. Furthermore, mathematical models demonstrate the singularity of our work in comparison to current literary materials and even describe some results using the classic Peyrard–Bishop model. All the established results contribute to the possibility of extending the approach to solve other nonlinear equations of fractional space–time derivatives in nonlinear sciences. The strategy that has been proposed recently is specific and is being employed to produce novel closed-form solutions for all many other FNLEEs.