Bifurcations, chaotic behaviour, sensitivity analysis, and diverse soliton structures for fractional nonlinear Kraenkel-Manna-Merle system adopting two techniques

The generalized Riccati equation mapping method and the modified extended tanh-function are the two analytical techniques that are used to solve the nonlinear fractional-order differential equations. The Riemann Liouville sense is used to define the fractional derivative in Jumaries. Through saturated ferromagnetic materials with negligible conductivity, a nonlinear ultrashort wave pulse moves according to the fractional Kraenkel-Manna-Merle system. A number of families of analytical solutions to the fractional Kraenkel-Manna Merle model are produced by applying the proposed methods. When the proper values are given to the parameters, these methods successfully recover both hyperbolic and trigonometric solutions. The contour, 3D, and 2D graphs are given to illustrate how the parameters affect these solutions. In addition, phase portrait characterization is performed and the system is converted into a planar dynamical structure. Furthermore, the dynamical system’s sensitivity examination verifies that even small changes to the starting circumstances will not significantly affect the solution’s stability.