Abundant M-fractional optical solitons to the pertubed Gerdjikov–Ivanov equation treating the mathematical nonlinear optics

In this paper, the perturbed Gerdjikov–Ivanov (GI) equation using a truncated M-fractional derivative is studied in mathematical nonlinear optics. We are explored its novel dark and other soliton solutions compared them with existing results. To obtain objective, two particular methods, modified extended $$\tanh$$ expansion method $$Exp_a$$ function method, implemented. exercise, an arrangement of exact solitons received as well verified by utilizing symbolic soft computations. The dynamical characteristics obtained results, along fractional parameter, also discussed via three-dimensional graphs. These suggested that employed methods impressive, determined smooth to many methods. work paper high importance regarding applications photonic crystal fibers physics.