Dynamics of new truncated M-fractional derivative wave structures to the nonlinear Zhiber-Shabat equation arising in variety of fields

Abstract In this work, we explore the different wave structures and the effect of fractional parameter to the nonlinear partial differential equation known as the nonlinear Zhiber-Shabat equation (ZSE). The model has a variety of applications in the mathematical community, including fluid dynamics, integral quantum field theory, nonlinear optics. The recently developed integration techniques known as generalized Riccati equation mapping method, Kumar-Malik method (KMM) and multivariate generalized exponential integral function approach are adopted. The suggested model is transformed into a nonlinear ordinary differential equation with the application of the truncated M-fractional derivative in order to get the intended results. The obtained structures are novel and expressed in the form of solitary wave solutions including hyperbolic, periodic as well as exponential function solutions under certain conditions. Various combinations and magnitudes of the physical parameters are employed to investigate the soliton solutions of the resultant system. Graphs are constructed by plotting the final solutions with the appropriate parameter values to elucidate the scientific interpretation and physical importance of the analytical findings.