Abstract :

The current study suggests a new generalization of highly dispersive nonlinear Schrӧdinger-type equation (NLSE) with perturbation terms. With polynomial refractive index, known by cubic-quintic-septic law (CQS) and Hamiltonian-type cubic perturbation terms, the new model includes eighth-order dispersion term. The generalized Riccati simplest equation method (RSEM) and the modified simplest equation method ( MSEM) are successfully utilized to analytically processing the fractional version of the considered NLSE. A diverse collection of bright, dark and singular optical solutions under some constraints, in form of hyperbolic, periodic, and rational-exponential are derived. Graphical interpretations of some obtained solutions are displayed. The two considered schemes, with different algorithms, show an influential mathematical tool for processing nonlinear fractional evolution equations.