Soliton solutions for fractional DNA Peyrard-Bishop equation via the extended-(G′/G2)-expansion method

In this article, the dynamical DNA equation comes into existence in the oscillatory chain, categorized as the Peyrard-Bishop model. The fractional Peyrard-Bishop model has been studied via beta-derivative and M-truncated derivative, for obtaining abundant solitary wave solutions. The proposed model is examined via M-truncated derivative for the first time in this article. The traveling wave transformation method is used to convert the proposed model into an ordinary differential equation. The extended(G'/G(2))-expansion method is applied to extract dark solitons, periodic solutions, singular solitons, combo solitons and rational solutions. On comparing our extracted solutions with the existing solutions in the literature, it is found that our results are new and not found in the literature. The obtained results are also explained graphically by plotting 3D plots to understand the phenomena of the proposed model.