Solitary wave solutions of the fractional Peyrard Bishop DNA model

Fractional order nonlinear partial differential equations are useful for detailing many practical models in multidisciplinary fields. In theory and numerical studies, recognizing solitary wave solutions to these equations is therefore preferable. The nonlinear properties of the fractional Peyrard Bishop DNA (FPBDNA) model make it relevant to several areas in integrable systems and nonlinear dynamics. The mathematical properties of the model, such as integrability and soliton solutions, have been examined by mathematicians to comprehend the behavior of nonlinear systems. In this article, we demonstrate how our techniques might be applied in a real life scenario like FPBDNA model. The soliton solutions to this model are determined using two effective analytical techniques namely the bernoulli sub ODE method and the modified khater method. These solutions have been obtained by using \(\beta\) $\beta$ and M-truncated derivatives. It is assumed that the obtained results have never been found in previous literature. The discovered solitons are smooth dark and bright, compactons, bell-shape and cuspon, peakon, anti-peakon, dark singular, bright singular, dark periodic singular, and kink-type solitons. The physical description is given using 2D and 3D for a finer perception.