Time-fractional of cubic-quartic Schrödinger and cubic-quartic resonant Schrödinger equations with parabolic law: various optical solutions

Abstract Schrödinger's nonlinear equation is a fundamental model in fiber optics and many other areas of science. Using the Jacobi elliptic expansion function method, the time-fractional cubic-quartic nonlinear Schrödinger equation and cubic-quartic resonant nonlinear Schrödinger equation are investigated. By applying the effective Jacobi elliptic expansion function method, optical soliton solutions such as bright, dark, singular, periodic singular, exponential, and Jacobi elliptic function solutions have been obtained. The effect of the time-fractional derivative on the solutions is also revealed. Graphical representations are illustrated to showcase the physical properties of raised solutions, providing a comprehensive understanding of the solutions’ functionality.