Analytical soliton solutions of the perturbed fractional nonlinear Schrödinger equation with space–time beta derivative by some techniques

Abstract

Nonlinear fractional-order evolution equations are fundamental strategies for simulating nonlinear phenomena on a large scale in technology, science, and engineering. This article considers the nonlinear space–time fractional perturbed nonlinear Schrödinger (NLS) equation defined in the sense of the beta-derivative, a widely used model to simulate nonlinear optics, ultra-short pulse lasers, optical communication systems, plasmas, and other domains. The model is converted into a nonlinear equation defined by fractional wave transformation. We construct diverse sorts of soliton solutions in the integration of rational, trigonometric, exponential, and hyperbolic functions with open parameters using the typical generalized exponential rational function (GERF) and the improved Bernoulli sub-equation function (IBSEF) schemes. Some standard shapes of waveforms, including parabolic soliton, kink, flat kink, bright-dark soliton, periodic soliton, breather, breathing periodic, singular periodic, breathing-like soliton, flat parabolic, and several other types of solitons, are determined. Periodic solitons under perturbations are required to understand ultra-short pulse lasers and long-distance optical communication systems. To validate the physical characteristics of the established solitons, we sketch 3D, 2D, and contour plots of the solutions using consistent values of the parameters. The techniques used in this study to extract inclusive and standard solutions are approachable, efficient, and speedier to compute the soliton solutions for nonlinear models in communication engineering and optics.