Detecting dynamical behaviors of solitary waves in the M-fractional Konopelchenko–Dubrovsky system with stability and sensitivity analysis

In this study, we investigate the solitary wave profiles of the Konopelchenko–Dubrovsky equation with the truncated M-fractional derivative. We employed the specific wave transformation to transform the studied partial differential equation (PDE) into a nonlinear ordinary differential equation (ODE), and then using the generalized Riccati equation mapping method to obtain various solitary wave profiles such as dark breather waves, bright breather waves, periodically oscillating waves, kink waves, etc., which are demonstrated graphically by two-dimensional (2D), three-dimensional (3D), and contour diagrams. The memory or hereditary effect in the model is discussed by varying the fractional derivative parameter. Moreover, we also discuss the stability, multistability, and sensitivity analysis of this model. All graphical illustrations are created using MATLAB and Maple. The observed solitary wave profiles demonstrate that this study is novel, reliable, simple, and could be applied straightforwardly across many scientific disciplines to understand the underlying complex wave interactions.