Optical solitons in the generalized space–time fractional cubic-quintic nonlinear Schrödinger equation with a [formula omitted]-symmetric potential

Abstract

In the presence of complexified parity reflection–time reversal (PT)−symmetric Scarff-II potential, we consider the generalized space–time fractional cubic-quintic nonlinear Schrödinger (FCQNLS) equation. By implementing fractal derivative variable transformation, we derive the fractional optical soliton solutions for the considered model. We consider two distinct forms of cubic-quintic nonlinearities, such as (i) focusing cubic-focusing quintic and (ii) defocusing cubic-focusing quintic for deriving the fractional optical soliton solutions. We investigate how modifying the temporal and space fractional-order parameters affects these fractional solitons. Our observations reveal that the rise in fractional-order parameters leads to the desired soliton profiles. We also examine further the effects of potential strengths on the fractional soliton profiles that are obtained.