LAUSR

The nonlinear fractional Schrödinger-Hirota equation is an important model in the field of physics, which is used to elaborate the propagation of optical solitons in optical fibers. In this presented work, the variational principle of the nonlinear fractional Schrödinger-Hirota equation is successfully established by using the semi-inverse method. A planar dynamical system is constructed by employing the Galilean transformation, and Hamiltonian function and sensitivity analysis are made. Moreover, the nonlinear fractional Schrödinger-Hirota equation is explored by using two novel mathematical approaches known as the modified fractional simplest equation method and the fractional extended rational sinh-cosh function approach. The solutions in the different forms, which include bright, dark, and periodic soliton families have been extracted in this study. Finally, the dynamic behavior of these new solutions is described by using a number of three-dimensional and two-dimensional graphs.