Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations

In nonlinear optics, photonics, plasma, condensed matter physics, and other domains, the space–time fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations associated with beta derivative have significant applications. The fractional wave transformation has been used to turn the space–time fractional nonlinear equations into integer order equations. To obtain optical soliton solutions relating to exponential, trigonometric, and hyperbolic functions and their integration with free parameters, the improved Bernoulli sub-equation function (IBSEF) scheme has been exploited. Different shapes of solitons have been extracted from the attained solutions, including kink, periodic, bell-shaped, anti-kink, dark-bright soliton, single kink type soliton, etc. A kink soliton is an optical shock front that keeps its shape while traveling through optical fibers. The characteristics of the solitons have been studied by describing profiles in 3D, 2D, contour, and density plots. The results imply that the IBSEF technique is simple, efficient, and capable of generating comprehensive soliton solutions of nonlinear models related to telecommunication and optics.