Analysis of some new wave solutions of DNA-Peyrard–Bishop equation via mathematical method

Abstract

The main goal of this paper is to extract the closed-form wave solutions by means of [Formula: see text]-expansion method to the DNA flow known as the Peyrard–Bishop model which describes the nonlinear interaction between neighboring displacements and hydrogen bonds. The aforementioned model is investigated for the time-fractional order and the fractional derivatives are used in the sense of conformable derivatives. The projected method provides additional generic and comprehensive wave solutions incorporated with physical parameters whose specific values reveal different shapes of the waveform such as periodic soliton, singular kink soliton, singular anti-kink soliton, and other different types of solitons. The obtained soliton solutions are novel, advanced, distinct, and relevant based on the available information in the literature which may be applied to more complex phenomena. The three-dimensional, two-dimensional, and contour plots of some of the attained results are sketched by assigning individual values of the parameters to scrutinize the dynamic behavior of the waves.